Question

In

Answer 1

Answer: There are 6720 ways to award 5 distinct prizes.

Step-by-step explanation:

Given : Total number of contestants are entered = 8

The number of distinct prizes = 5

Since , the order of warding the prize matters , So we use Permutations.

The number of permutation of selecting r things out of n things = $^nP_r=\dfrac{n!}{(n-r)!}$

Here , n= 8 and r=5

Then, the number of different ways 5  distinct prizes can be awarded

=$^8P_5=\dfrac{8!}{(8-5)!}$

$=\dfrac{8\times7\times6\times5\times4\times3!}{3!}=6720$

Hence, there are 6720 ways to award 5 distinct prizes.