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There are 24 members on a swim team. How many different combinations of 5 swimmers can be chosen to sit in the front row for a team photo?

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jushmk
This is a question combinations.

Number of combination to choose 5 swimmers from 24 members = 24C5 = 24!/[5!*(25-5)!] = 42504

Therefore, there are 42504 ways in which 5 swimmers can be chosen to sit on the front row from 24 members swim team.
JeanaShupp

Answer: 42504

Step-by-step explanation:

We know that the combination of n things taken x at a time is given by :-

[tex]^nC_x=\dfrac{n!}{x!(n-x)!}[/tex]

Given : There are 24 members on a swim team.

i.e. n= 24

Then, the number of different combinations of 5 swimmers can be chosen to sit in the front row for a team photo :-

[tex]^{24}C_5=\dfrac{24!}{5!(24-5)!}=\dfrac{24!}{5!19!}=42504[/tex]

Therefore, the number of different combinations of 5 swimmers can be chosen to sit in the front row for a team photo = 42504

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