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

Answer:

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

Step-by-step 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

= $^{13}C_{6}$

= $\frac{13!}{(6!)(13-6)!}$

= $\frac{13\times 12\times 11\times 10\times 9\times 8\times 7!}{6!\times 7!}$

= $\frac{13\times 12\times 11\times 10\times 9\times 8}{6\times 5\times 4\times 3\times 2\times 1}$

= $\frac{1235520}{720}$

= 1716

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