MILBURN, Circuit Judge.

Defendant Clifford Lee appeals his jury conviction and the judgment entered thereon for conspiracy to possess cocaine with intent to distribute and distributing cocaine in violation of 21 U.S.C. § 846 and 841(a)(1). On appeal, the issues are (1) whether the evidence presented at trial was sufficient to support defendant's conviction, and (2) whether the district court's instruction on deliberate ignorance violated the Due Process Clause of The Constitution of the United States by impermissibly shifting the burden of proof from the prosecution to defendant. For the reasons that follow, we affirm.

I. A.

This case involved approximately eighteen conspirators engaged in transporting large quantities of cocaine from Miami, Florida, to Detroit, Michigan, and distributing the cocaine in the Detroit area.

One of the government's witnesses at defendant's trial was coconspirator Jim Dortch. Dortch testified based upon the terms of his Federal Rule of Criminal Procedure 11 plea agreement with the government. Dortch testified that it was not unusual for him to deal in quantities of cocaine as large as 40 kilograms and that the cost of 20 kilograms of cocaine varied between $320,000 and $800,000. Dortch also testified that he had known defendant for approximately ten to twelve years, and he described defendant as his "best friend in the world." J.A., tr. p. 8. Dortch stated that when he and defendant first met, Dortch was struggling to make ends meet with the income from his motorcycle shop. As the shop proved unprofitable, he began dealing in cocaine during 1987.

After Dortch began dealing in cocaine, he testified that defendant Lee accompanied him to late night or early morning meetings with other drug dealers. Dortch described defendant as his "bodyguard." J.A., tr., p. 12. Dortch stated that, for safety reasons, defendant would stay in the car while Dortch conducted the drug transactions. This was because the other drug dealers were less likely to try something if they knew that both he and defendant were there but were not together at the same location. During this period of time, defendant was a firefighter for the Detroit Fire Department. According to Dortch, defendant was routinely available to help him because defendant had "a really lax schedule," working approximately nine days per month.

Defendant Lee also wired money through Western Union and rented cars for Dortch at his request, since Dortch did not have a credit card and could not rent cars for himself. Dortch also testified that, on several occasions, defendant delivered packages of cocaine or cash for him. Dortch testified that the packages were always tightly sealed when he gave them to defendant and that he did not expressly tell defendant that the packages he was delivering contained either large sums of cash or cocaine. Specifically, Dortch testified that, on occasion, he sent defendant to one of his customers, Maurice Wilson, with a package containing five kilograms of cocaine, but he and defendant did not discuss the contents of the packages.

In October 1989, defendant Lee flew with Dortch to Miami, Florida, to meet with one of Dortch's suppliers, Pepe Nunez. During the meeting, Dortch and Nunez had a heated argument about money shortages involved with their cocaine deals. After defendant heard some of the argument, he walked into Nunez's living room and began playing the piano. Dortch testified that during these discussions, the word cocaine was very rarely mentioned; however, money was discussed openly and the word kilogram or kilos was also used.

Dortch further testified that at the bike shop, the word cocaine was never used in defendant's presence. Rather, the words "motors" or "carburetors" were used to refer to cocaine. Dortch admitted that as part of the operation of the bike shop, it would be unusual for him to work on more than 20 motorcycles per year. However, defendant was present for discussions between Dortch and his coconspirators when delivery of 40 carburetors or motors was discussed. Dortch testified that as part of his operation of the motorcycle shop, he never placed an order for 40 motors or carburetors, even on his best day. According to Dortch, defendant overheard at least five or six such discussions between himself and his coconspirators, particularly Manuel Garcia.

Dortch also had frequent arguments in defendant's presence with Manuel Garcia. These arguments occurred at Dortch's motorcycle shop and were frequent and loud. On one of these occasions, defendant allegedly told Dortch that a public race course in Memphis, Tennessee, would be a particularly good place to conduct a cocaine transaction.

On another occasion, defendant accompanied Dortch to the home of another coconspirator, Maurice Wilson, to pick up money that Wilson owed Dortch as the result of a prior cocaine transaction. Wilson counted out $19,000 in cash for Dortch in defendant's presence. Dortch testified that Wilson was an almost daily visitor to his motorcycle shop, where he would arrange for purchases of 20 to 30 kilograms. Dortch said that these discussions took place in front of defendant and that "carburetors" and "money" were discussed in lieu of cocaine. According to Dortch, he never ordered more than four or five carburetors at one time for his motorcycle business.

In November 1989, defendant Lee rented a car and, at Dortch's request, took two duffle bags containing approximately $800,000 in cash to Florida. Defendant testified that he traveled to Florida with a companion, Roxanne Sams, and that the purpose for the trip was to visit Disney-world in Orlando. Defendant further testified that, as agreed, he called Dortch to arrange for the duffle bags to be picked up when he arrived at his hotel in Orlando.

Defendant's rental car broke down in Orlando, and the rental car company informed defendant that he would need to travel to Miami to obtain a replacement. When defendant notified Dortch that his rental car had broken down and that he would need to travel to Miami, Dortch arranged for a trucker to pick up defendant in Orlando and take him and the two duffle bags to Miami. As it turned out, Miami was the ultimate destination of the duffle bags and the cash they contained.

The unknown trucker drove defendant to the Holiday Inn in North Miami, Florida. Upon his arrival, defendant telephoned Dortch who arranged for two men to pick up the duffle bags. Defendant testified that after the two duffle bags were picked up, the trucker drove him back to Orlando because there were no rental cars available in Miami.

Pepe Nunez, one of the coconspirators, testified that defendant delivered a large sum of money to his home in Miami in the late fall of 1989. Nunez testified that Dortch called him on the telephone and stated that his "right hand man" would be delivering the money. Nunez stated that he counted out the money while defendant was present and that he remembered defendant playing the piano at his house.

Defendant also wired, at Dortch's request, a total of $22,000 to two separate individuals, which moneys were intended for ultimate receipt by Nunez in payment for shipments of cocaine to Dortch in Detroit. Moreover, Dortch testified that while he was running the motorcycle shop, he occasionally bought small gifts for defendant, and after he began dealing cocaine, he bought several thousand dollars worth of clothes and jewelry for defendant. He also spent several thousand dollars on entertainment, trips, restaurants, and hotels for defendant.

Another coconspirator, Ronald Vance, testified that coconspirator Donald McDonald told him that defendant transported cocaine "around town [Detroit] for Dortch." Vance testified that defendant was referred to as Dortch's "boy" or "right hand man." Vance testified that sometime in late 1989, he was present at the home of another coconspirator, John Thompson, when Dortch and defendant arrived with a kilogram of cocaine and that defendant was present when Thompson opened the package of cocaine. Vance also testified that on one occasion he picked up two kilograms of cocaine from coconspirator Manuel Garcia for Dortch. Dortch and defendant drove to Vance's home in Dortch's Corvette convertible in order to pick up the cocaine. Vance testified that he gave the cocaine, which was in a small bag, to defendant and that defendant passed the cocaine over to Dortch.

B.

On March 28, 1991, defendant Lee was charged in Count One of a six-count indictment, the second superseding indictment, with conspiring with his eighteen codefendants to possess cocaine with intent to distribute and distributing cocaine in violation of 21 U.S.C. § 846 and 841(a)(1). A jury trial commenced on October 17, 1991. The trial concluded on November 19, 1991, and the jury returned a guilty verdict against defendant on November 22, 1991.

On February 20, 1992, defendant was sentenced to 120 months' imprisonment to be followed by five years' supervised release. This timely appeal followed.

II. A.

Defendant Lee argues that insufficient evidence was presented at trial to support his conviction. Specifically, defendant asserts that the government did not prove that he intentionally joined the conspiracy. Rather, he asserts that he has been convicted merely because of his association with Dortch.

The standard of review used in determining the sufficiency of the evidence supporting a guilty verdict is "whether after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt." United States v. Bourjaily, 781 F.2d 539, 544 (6th Cir. 1986), aff'd, 483 U.S. 171, 107 S.Ct. 2775, 97 L.Ed.2d 144 (1987) (quoting Jackson v. Virginia, 443 U.S. 307, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979)). The essential elements of the crime of conspiracy are:

(1) that the conspiracy described in the indictment was willfully formed, and was existing at or about the time alleged; (2) that the accused willfully became a member of the conspiracy; (3) that one of the conspirators thereafter knowingly committed at least one of the overt acts charged in the indictment, at or about the time and place alleged; and (4) that such overt act was knowingly done in furtherance of some object or purpose of the conspiracy as charged.

United States v. Poulos, 895 F.2d 1113, 1117 (6th Cir. 1990) (quoting United States v. Meyers, 646 F.2d 1142, 1143-44 (6th Cir. 1981)). More specifically, to sustain a conviction under 21 U.S.C. § 846, the government is required to prove the existence of an agreement to violate the drug laws and that each conspirator knew of, intended to join, and participated in the conspiracy. United States v. Sanchez, 928 F.2d 1450, 1457 (6th Cir. 1991).

"The existence of a criminal conspiracy need not be proven by direct evidence, a common plan may be inferred from circumstantial evidence." Poulos, 895 F.2d at 1117. Circumstantial evidence standing alone can sustain the jury's verdict, and such circumstantial evidence need not remove every reasonable possibility except that of guilt. United States v. Townsend, 796 F.2d 158, 161 (6th Cir. 1986) (citing United States v. Stone, 748 F.2d 361, 362 (6th Cir. 1984)).

Moreover, once the existence of a conspiracy has been proven, only slight evidence is necessary to implicate a defendant. Poulos, 895 F.2d at 1117. Further, proof of a formal agreement among the conspirators is unnecessary; a tacit or mutual understanding among the parties is sufficient to show a conspiracy. Sanchez, 928 F.2d at 1457. In addition, "[e]very member of the conspiracy need not be an active participant in every phase of the conspiracy, so long as he is a party to the general conspiratorial agreement." Id. (quoting United States v. Christian, 786 F.2d 203, 211 (6th Cir. 1986)).

In this case, after viewing the evidence in the light most favorable to the government, there is more than ample evidence from which the jury could have inferred that defendant was aware of and participated in the conspiracy. Defendant places great weight on Dortch's testimony that he never told defendant that the packages he delivered contained cocaine and that defendant remained in the car while acting as Dortch's "bodyguard" during drug transactions. Thus, defendant argues that the government failed to show that he was aware of or participated in the conspiracy and asserts that he was convicted of conspiracy due to his friendship with coconspirator Dortch. A defendant cannot be convicted of conspiracy merely on the grounds of guilt by association, and mere association with the members of a conspiracy without the intention and agreement to accomplish an illegal objective is not sufficient to make an individual a conspirator. See United States v. Melchor-Lopez, 627 F.2d 886, 891 (9th Cir. 1980).

However, defendant Lee did more than merely associate with Dortch and other coconspirators. In this case, defendant accompanied Dortch to late-night drug deals. Further, defendant was present with Dortch on at least one occasion when a package of cocaine was opened in front of him. On another occasion, one of Dortch's "customers" paid Dortch $19,000 in cash in defendant's presence. Dortch testified that amounts of money were discussed openly in defendant's presence, and although the cocaine was discussed using such code words as "motors" and "carburetors," the numbers discussed were far greater than those which Dortch could have used in the course of his legitimate business. In addition, defendant delivered approximately $800,000 in cash in two duffle bags to Dortch's supplier in Miami. Although defendant testified that he never looked in either of the duffle bags and was unaware of their contents, the jury was free to disbelieve defendant's testimony in this regard.

From all of this evidence, the jury could have inferred that defendant was aware of, participated in, and intended to further the conspiracy to possess and distribute cocaine. Contrary to defendant's assertion, the evidence in this case is not so one-sided that the jury would have had to conclude that he was an unfortunate and unwitting spectator to the drug conspiracy.

Defendant also argues that the evidence presented at trial was insufficient to sustain his conviction because the evidence presented showed multiple conspiracies, whereas he was convicted of participating in a single conspiracy. Defendant asserts that this resulted in a variance between the charges in the indictment and the evidence presented at his trial.

If an indictment alleges one conspiracy, but the evidence can be construed as only supporting a finding of multiple conspiracies, a variance results. United States v. Warner, 690 F.2d 545, 548 (6th Cir. 1982). However, even if a variance exists, it does not constitute reversible error "unless it prejudice[s] [the defendant's] substantial rights." United States v. Guerra-Marez, 928 F.2d 665, 671 (5th Cir.), cert. denied, ___ U.S. ___, 112 S.Ct. 322, 116 L.Ed.2d 263 and ___ U.S. ___, 112 S.Ct. 443, 116 L.Ed.2d 461 (1991) (quoting United States v. Richerson, 833 F.2d 1147, 1154-55 (5th Cir. 1987)). Moreover, "[i]f the government proves multiple conspiracies and a defendant's involvement in at least one of them, then clearly there is no variance affecting that defendant's substantial rights." Guerra-Marez, 928 F.2d at 672 (quoting United States v. L'Hoste, 609 F.2d 796, 801 (5th Cir.), cert. denied, 449 U.S. 833, 101 S.Ct. 104, 66 L.Ed.2d 39 (1980)).

In this case, the government proved the existence of a single "chain" conspiracy to distribute narcotics. In this regard, we have stated that

[c]onspiracies to distribute narcotics, which normally involve numerous sales and resales of drugs until they reach the ultimate consumers, are often "chain" conspiracies.

Warner, 690 F.2d at 549.

The conspiracy at issue here involved the shipment of cocaine from the "supplier," Nunez, in Miami, Florida, to the "distributor," Dortch, in Detroit, Michigan. Defendant's role in the conspiracy involved both assisting Dortch in the distribution of the cocaine to "customers" in Detroit as well as, on at least two occasions, aiding Dortch in delivering cash to his supplier in Miami. Although Dortch may have had several "customers" in the Detroit area, each of these customers were part of the same "chain" conspiracy, the object of which was the transportation of cocaine from Florida to Michigan and the distribution of the cocaine in the Detroit area. Thus, defendant's assertions that the government proved the existence of multiple conspiracies rather than a single conspiracy and that, as a consequence, a variance resulted between the charges in the indictment and the evidence presented at trial are meritless.

Finally, defendant also argues that the evidence was insufficient to support his conviction because the principal witnesses against him, Dortch, and Nunez, had entered into plea agreements with the government, which required them to testify for the government against defendant. Thus, defendant argues that their testimony lacks credibility. However, "[a]ttacks on witness credibility are simple challenges to the quality of the government's evidence and not the sufficiency of the evidence." Sanchez, 928 F.2d at 1457 (quoting United States v. Adamo, 742 F.2d 927, 932 (6th Cir. 1984), cert. denied sub nom. Freeman v. United States, 469 U.S. 1193, 105 S.Ct. 971, 83 L.Ed.2d 975 (1985).

B.

Defendant argues that the district court's instruction on deliberate ignorance violated due process because the instruction as given had the effect of shifting the burden of proof from the prosecution to defendant. At trial, the district court gave the following instruction to the jury:

No one can avoid responsibility for a crime by deliberately ignoring the obvious. If you are convinced that a defendant deliberately ignored a high probability that he was assisting another in a drug transaction, then you may find he knew what he was doing. But to find this, you must be convinced that the defendant was aware of a high probability that he was assisting another in a drug transaction, and that the defendant deliberately closed his eyes to what was obvious. Carelessness or negligence or foolishness on his part is not the same as knowledge and is not enough to convict.

J.A., tr., pp. 114-15. Specifically, defendant asserts that the deliberate ignorance instruction was improperly utilized in this case because (1) it "strikes at the heart of [defendant's] defense theory of the case," (2) it "establishes some type of negligence or recklessness standard" which undercuts the beyond a reasonable doubt standard, and (3) it shifts the burden of proof to defendant to establish his innocence. Appellant's brief, pp. 19-21.

On appeal the standard of review of a district court's charge to a jury is "whether the charge taken as a whole, fairly and adequately submits the issues and applicable law to the jury." United States v. Buckley, 934 F.2d 84, 87 (6th Cir. 1991) (quoting United States v. Martin, 740 F.2d 1352, 1361 (6th Cir. 1984)). "[I]t is clear that no single provision of the jury instruction can be read in isolation, and that the charge must be considered as a whole." United States v. Horton, 847 F.2d 313, 322 (6th Cir. 1988).

Defendant's argument that the deliberate ignorance instruction undermined the reasonable doubt standard and shifted the burden of proof from the prosecution to him has been rejected by this court. In United States v. Lawson, 780 F.2d 535, 542 (6th Cir. 1985) (per curiam), we upheld a "willful ignorance" instruction which was very similar to the instruction given in this case. We found that by using the "willful ignorance" instruction, the district court did not "lessen the burden placed on the government to prove the necessary elements of the offense beyond a reasonable doubt." Id. Furthermore, in United States v. Gullett, 713 F.2d 1203, 1212 (6th Cir. 1983), cert. denied, 464 U.S. 1069, 104 S.Ct. 973, 79 L.Ed.2d 211 (1984), this court upheld an instruction that "the element of knowledge . . . may be inferred from proof that the defendants `acted with a reckless disregard for the truth or with a conscious purpose to avoid learning the truth about the unlawful transaction'. . . ." Id. We stated that "[t]he instruction does not authorize a conviction based on negligent behavior, but rather prevents a criminal defendant from escaping conviction merely by deliberately closing his eyes to the obvious risk that he is engaging in unlawful conduct." Id.

Furthermore, there was evidence of deliberate ignorance in the record which permitted the district court to utilize the instruction. First, defendant himself testified that although he transported $800,000 in cash in two duffle bags from Detroit to Miami, he was unaware that the bags contained the moneys because he never looked in them. Second, defendant also testified that although he was present in Pepe Nunez's home when Nunez and Dortch began arguing about drugs and money, he never heard their argument, even though he was standing on the other side of an open archway from Nunez and Dortch, at least for a short period of time before he began playing Nunez's piano. Defendant testified that he did not hear the argument over the piano. However, Dortch testified that the argument had been underway for approximately one-half hour before defendant began playing the piano.

Accordingly, we hold that the district court's deliberate ignorance instruction was properly utilized because there was evidence showing deliberate ignorance presented at trial. Furthermore, the instruction, drawn directly from Sixth Circuit Pattern Jury Instruction 2.09, which we expressly approve under the facts of this case, did not deprive defendant of a fair trial, and, therefore, did not deprive him of due process.

III.

For the reasons stated, the judgment of the district court is AFFIRMED.