Question

How many ways can we award a 1st, 2nd and 3rd place prize among eight contestants?

56 ways

none of these

40320 ways


336 ways

Answer 1

Total number of ways are 336.

Explanation:

It is required to find the number of ways in which we can award a 1st, 2nd and 3rd place prize among eight contestants. It means we need to find the number of permutations. We need to find
`^8P_3`.

Here, r = 3

So,

`^nP_r=(n!)/((n-r)!)\\\\^8P_3=(8!)/((8-3)!)\\\\^8P_3=(8!)/(5!)\\\\^8P_3=(8* 7* 6* 5!)/(5!)\\\\^8P_3=336`

So, there are 336 ways.