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 ?

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.
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It can be done is 17P3 ways.


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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.