Hi ModularArithmetic,
This is a layered 'Combination Formula' question. Normally, you're asked to figure out the total number of possible combinations, but here you're asked to 'work back' and figure out one of the pieces of the overall calculation.
Based on the information in the prompt, we know....
1) The store sells 7 different colors of balloon and X different colors of confetti.
2) Jim is going to buy 3 different colors of balloon and 2 different colors of confetti
3) There are 350 different combinations that Jim can purchase (based on his 'restrictions')
We can go about solving this question in pieces:
First, we'll deal with the balloons. There are 7 different colors and Jim is going to choose 3. Since the 'order' of the colors does NOT matter, we can use the Combination Formula:
N!/[K!(N-K)!] where N = 7 and K = 3
7!/[3!4!] = 35 different combinations of balloons.
Using this information, and the fact that there are 350 different OVERALL combinations, we can figure out the number of combinations of confetti...
35(X) = 350
X = 10 different combinations of confetti.
Next, we know that Jim is going to choose 2 different types of confetti, so that is the "K" in this next calculation...
N!/[2!(N-2)!] = 10
You might recognize this pattern from another question or you might use the answer choices to your advantage (one of them IS the value of N here), but you'll find that N = 5
5!/2!3! = 10 different combinations of confetti.
Final Answer:
GMAT assassins aren't born, they're made,
Rich