Question

There are eight runners in the 100-meter dash. In how many ways can the runners finish in first, second, and third place?
6
72
120
336

Answer 1

Answer is below.......

Answer 2

Answer: 336

Step-by-step explanation:

Given : The total number of runners = 8

The number of positions = 3

Since for awarding prize, the order of winners matters.

So by permutations ,the number of possible ways to award 3 prizes will be

$^8P_3=\dfrac{8!}{(8-3)!}=8\times7\times6=336$

Therefore , the total number of ways by which runners finish in first, second, and third place is 336.