Question

Thirty-six people in student council are running for the offices of president and vice-president. In how many different ways can those offices be assigned?

Answer 1

1,260
578
71

Answer 2

@nbouscal how do i do this one

Answer 3

Since they are two different offices, order matters, so it is a permutation. The formula for a permutation \(_mP_n=\dfrac{m!}{(m-n)!}\), so this one is \(_{36}P_2=\dfrac{36!}{(36-2)!}=\dfrac{36!}{34!}=36\times35=1260\)

Answer 4

Here is a more intuitive way to think about this if you haven't learned permutations yet. First, pick someone for the office of president. There are 36 different options. Second, pick someone for the office of vice president. You can't choose the person that you already picked as president, so you have 35 options. So then you multiply the two to get your total number of options, 1260.

Answer 5

thank you