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 = [tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Here , n= 8 and r=5
Then, the number of different ways 5 distinct prizes can be awarded
=[tex]^8P_5=\dfrac{8!}{(8-5)!}[/tex]
[tex]=\dfrac{8\times7\times6\times5\times4\times3!}{3!}=6720[/tex]
Hence, there are 6720 ways to award 5 distinct prizes.
