Question

There are 50 runners in a race. how many ways can the runner finish first, second and third

Answer 1

50 x 49 x 48 = 117,600 ways
You have 50 possible for 1st, 49 for 2nd, 48 for 3rd
or
Permutations 50P3 = 117,600

Answer 2

Hence, the number of ways are:

117600

Explanation:

There are 50 runners in a race.

The number of ways can the runner finish first, second and third is:

we have to apply permutation since we have to choose 3 players out of the 50 players who are in a race and arrange them according to their ranks as well.

Hence, the number of ways it could be done is:

`50_(P_3)=(50!)/((50-3)!)\\\\50_(P_3)=(50!)/(47!)\\\\50_(P_3)=50* 49* 48\\\\50_(P_3)=117600`

Hence, the number of ways are:

117600