Question

there are 17 people in a club . How many ways can 3 of them be chosen as president,vice president 'and Secretary? how many can 2 of them be chosen to be on the student Senate ?

Answer 1

We have to choose 3 people at random and give them separate posts.

Just to choose 3 from 17 : use combination

To choose 3 and give separate posts: use permutation

So we have to use permutation.
________________________

It can be done is 17P3 ways.

`{}^(17) P_3 = (17!)/((17-3)!) \\ = (17!)/(14!) \\ =17 * 16 * 15 \\ = 4080`

__________________________

From the chosen 3, you have to select 2 at random for Senate.

Choose 2 from 3.

Number of ways = 3C2 = 3! / [ 2! × (3-2)! ] = 3! / 2! = 3

You can do it in 3 ways.