Question: There are 6 men and seven woman in a club. A committee is to be formed. How many ways can we select a committee of five persons?
Answer: C(13,5) or 13! / ((8!)(3!))
That is the answer given in the book, but my answer was originally P(13,5), or 13*12*11*10*9.
I thought my answer was right because there are P(13,5) permutations to fit five people into the committee from 13 total people, why is it a combination problem and not a permutation problem?
Thanks
Best Answer
Yes, there are $P(13,5)$ ways to choose five people to line up in a certain order to form the committee. But you count each committee $5!$ times (for example {Amy, Bob, Carl, Doug, Ed} is the same as {Ed, Doug, Carl, Bob, Amy}, but you counted them as being different). So we need to divide by $5!$. By the way, I think you have a typo: the answer is $C(13,5) = 13!/(8!5!)$.