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
= [tex]^{13}C_{6}[/tex]
= [tex]\frac{13!}{(6!)(13-6)!}[/tex]
= [tex]\frac{13\times 12\times 11\times 10\times 9\times 8\times 7!}{6!\times 7!}[/tex]
= [tex]\frac{13\times 12\times 11\times 10\times 9\times 8}{6\times 5\times 4\times 3\times 2\times 1}[/tex]
= [tex]\frac{1235520}{720}[/tex]
= 1716
Therefore, 6 swimmers in the first heat can be arranged in 1716 different ways.
