[GMAT math practice question]
i, j, and k are non-negative integers such that i+j+k=3. If p, q, and r are three fixed, but different, prime numbers, how many different values of p^iq^jr^k are possible?
A. 8
B. 9
C. 10
D. 11
E. 12
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The number of possible values of p^iq^jr^k is equal to the number of solutions of the equation i + j + k = 3.
The solution set of the equation i + j + k = 3 includes all permutations of (3,0,0), (2,1,0), and (1,1,1).
The number of permutations of (3,0,0) is 3!2! = 3.
The number of permutations of (2,1,0) is 3! = 6.
The number of permutations of (1,1,1) is 1.
Therefore, the number of solutions of the equation i+j+k=3 is 3 + 6 + 1 = 10.
Therefore, the answer is C.
Answer: C