How many ways that you can choose 3 desserts from a menu of 10?

Question

Anton · Accepted Answer

Just to clarify: the original reviewer's answer - C(10,3) - is indeed incorrect. 

More specifically, C(10,3) represents a number of ways to pick 3 DISTINCT desserts. The problem statement does not suggest that the desserts should be unique; moreover, it's very natural to order three identical desserts!

I believe the correct answer to be a sum of
C(10,3) /* number of ways to pick 3 distinct desserts */ +
10 * 9  /*number of ways to pick 2 matching and 1 distinct dessert */ +
10 /* number of ways to pick 3 matching desserts */
= 220

Sigiloso · Answer

C (10, 3) = 120 - This is very simple

Chris · Answer

If order matters (it would to me if I were eating them), and repetition is allowed, the answer would be 1,000 since you can choose any of the 10 for the first, second and third dessert resulting in 10 X 10 X 10 possible dessert sequences.

Curtis · Answer

10x10x10 = 1000

Sigiloso · Answer

10*9*8 = 720 combinations

Sigiloso · Answer

45 I suppose

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