Question

a swim meet has 13 contestants signed up for a 100 meter butterfly event. how many different ways can the top 6 contestants place

Answer 1

78 because 13 times 6 is 78

Answer 2

Answer: 1235520

Explanation:

Given : A swim meet has 13 contestants signed up for a 100 meter butterfly event.

To find the number of ways can the top 6 contestants place, we use permutations because order to place them matters here.

We know that the number of permutations of n things such that r things taken at time is given by :_

`^nP_r=(n!)/((n-r)!)`

Then, the number of different ways can the top 6 contestants place out of 13 contestants will be:_

`^(13)P_6=(13!)/((13-6)!)\\\\=(13*12*11*10*9*8*7!)/(7!)\\\\=1235520`

Hence, the number of different ways can the top 6 contestants place = 1235520