How many ways can a committee of four students be selected from a 15-member club?
A)15!/44!
B)15!/(4! × 11!)
C)15 × 14 × 13
D)B and C

Question

Quizplus · Accepted Answer

This is a combination problem where order doesn't matter. The formula for selecting a committee of k members from a set of n members is nCk = n!/((n-k)!k!). In this case, we want to select 4 members from a set of 15, so the formula gives us 15C4 = 15!/((15-4)!4!) = 15!/11!4! = 15 × 14 × 13 × 12 / 4 × 3 × 2 × 1 = 1365. Therefore, the answer is B, which is the formula 15!/(4! × 11!). The answer C, which is simply the multiplication of the first three numbers, is only valid if order matters (i.e. selecting a president, vice-president, etc.) which is not stated in the problem. Answer A is not even a valid formula.

How Many Ways Can a Committee of Four Students Be