How many ways are there to choose a half dozen donuts from 10 varieties a) If there are no two donuts of the same variety. b) If there are at least two varieties. c) If there must be at least one but no more than 4 glazed.

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Mathematics

Braveheart

29 April, 14:26

How many ways are there to choose a half dozen donuts from 10 varieties a) If there are no two donuts of the same variety. b) If there are at least two varieties. c) If there must be at least one but no more than 4 glazed.

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Vanessa Best · Answer 1

If multiples are allowed (like "10 plain, two chocolate"), then for each of 12 donuts there are 21 possibilities.

That is 21 x 21 x 21 ... x 21 (12 terms in all) = 21^12