Question

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?

Answer 1

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.

Answer 2

Answer: 42504

Explanation:

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

`^nC_x=(n!)/(x!(n-x)!)`

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 :-

`^(24)C_5=(24!)/(5!(24-5)!)=(24!)/(5!19!)=42504`

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