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

Question

Quizplus · Accepted Answer

This is a combination problem, where we need to select 4 students from 15 without regard to order. Therefore, we can use the formula for combinations: nCr = n!/(r!(n-r)!), where n is the total number of students and r is the number we are selecting. Therefore, the number of ways to select a committee of 4 students from a 15-member club is 15!/(4!(15-4)!) = 15!/(4!11!) which is equivalent to choice B. Choice C is simply the calculation of 15 ×14 ×13 without regard to order, which is not quite the same as the combination formula used in choice B. Choice A is not correct as it involves a factor of 44 which is not present in the problem. Therefore, the best choice is B.

How Many Ways Can a Committee of Four Students Be