Question

Ms. Lunette has 18 students in her class. She wants to send 3 of these students to pick up books for the class.


How many combinations of 3 students can she choose?

Answer 1

The number of possible combinations is given by

... C(18, 3) = 18!/(3!(18-3)!) = 18·17·16/(3·2·1) = 816 . . . . possible combinations

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There are 18 ways to choose the first one; 17 ways to choose the second one, and 16 ways to choose the 3rd one. The same 3 students can be chosen in any of 3! = 6 different orders, so the product 18·17·16 must be divided by 6 to get the number of possible combinations in which order doesn't matter.