After the tryouts for the volleyball team, the coach selects 14 people to join the team. Due to a problem with transportation, only 7 people can travel. In how many ways can the coach pick the people to go?
Question
After the tryouts for the volleyball team, the coach selects 14 people to join the team. Due to a problem with transportation, only 7 people can travel. In how many ways can the coach pick the people to go?
Solution
This is a problem of combinations. The coach is choosing 7 people out of a group of 14. The order in which the people are chosen does not matter, so we use the combination formula:
C(n, k) = n! / [k!(n-k)!]
where:
- n is the total number of options (in this case, 14 people),
- k is the number of options to choose (in this case, 7 people),
- "!" denotes factorial, meaning the product of all positive integers up to that number.
So, the number of ways the coach can pick the people to go is:
C(14, 7) = 14! / [7!(14-7)!] = 3432 ways.
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