Question

Eight prizes are to be given to eight different people in a group of eighteen. In how many ways can a first prize, a second prize, a third prize and five fourth prizes be given? how many ways

Answer 1

First we select 8 people from a group of 18. And the we permute the 8 prizes among these people.

The number of ways of selecting 8 people from a group of 18 = 18C8

The number of ways of permuting the 8 prizes (in which 5, 4th prizes are identical) among 8 given people = 8! / 5!

So the number of ways in which a first prize, a second prize, a third prize and five fourth prizes be given is

18C8 x 8! / 5! = 43758 x 336 = 1,47,02,688 ways

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