Question

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

Answer 1

Answer:

Total number of ways are 336.

Step-by-step 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,

$^nP_r=\dfrac{n!}{(n-r)!}\\\\^8P_3=\dfrac{8!}{(8-3)!}\\\\^8P_3=\dfrac{8!}{5!}\\\\^8P_3=\dfrac{8\times 7\times 6\times 5!}{5!}\\\\^8P_3=336$

So, there are 336 ways.