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PS - combinations

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PS - combinations

by oks » Sun Jul 05, 2009 2:57 pm
A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If
each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how
many different dessert platters could the restaurant offer?
A. 8
B. 12
C. 15
D. 21
E. 27

OA is E.

My approach - 8!/6!2! = 28

What am I missing? Thanks!
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by GMATQuantCoach » Sun Jul 05, 2009 6:30 pm
There are 2 cases. The platter can have 1 kind of cheese and 1 kind of fruit, or 2 kinds of cheese and 2 kinds of fruit.

Case 1: 1 kind of cheese with 1 kind of fruit
Choose the cheese, and then choose the fruit
2C1 * 6C1 = 2 * 6 = 12

Case 2: 2 kinds of cheese with 2 kinds of fruit
Choose the cheese, and then choose the fruit
2C2 * 6C2 = 1 * 6!/(2!*4!) = 6*5/2! = 15

Add them up.
12 + 15 = 27

E is the answer.
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