Question

A swim meet has 13 contestants signed up for the 100-meter butterfly event. The first heat has 6 swimmers. How many different ways can the contestants be arranged in the first heat?

Answer 1

6 swimmers in the first heat can be arranged in 1716 different ways.

Explanation:

A swim meet has 13 contestants signed up. To calculate the arrangement of first 6 swimmers in first heat we will use combinations because order doesn't matter.

So to select 6 swimmers out of 13 contestants number of different ways

=
`^(13)C_(6)`

=
`(13!)/((6!)(13-6)!)`

=
`(13* 12* 11* 10* 9* 8* 7!)/(6!* 7!)`

=
`(13* 12* 11* 10* 9* 8)/(6* 5* 4* 3* 2* 1)`

=
`(1235520)/(720)`

= 1716

Therefore, 6 swimmers in the first heat can be arranged in 1716 different ways.