A committee of 5 people is to be formed from a group of 7 women and 4 men. How many possible committees can be formed if: the committee then must chose a president and a vice president, how many ways could these two positions be chosen?

Question

why is it permutations not combination? I randomly tried 5P2 and got the right answer, but I don't get why it isnt 5C2?

Thanks in advance

Answer 1

For pres and vp

John and Joe is different from
Joe and John

This is why it is a permutation.

on a commitee Joe and John are the same choice as John and Joe which requires a combination.

Answer 2

Your question is not clear at all.
Are we first selecting the committees, then picking the president and vp ?

number of committees
= C(11,5) = 462

to pick a president , then vice president, order does matter, so
11x10 = 110 or P(11,2)

if we are picking the pres and vpres from the 5, then
5x4 = 20 or P(5,2)