From a group of 9 people, select the best 3 players to represent the group to participate in the team competition. How many total possibilities are there?
Question
From a group of 9 people, select the best 3 players to represent the group to participate in the team competition. How many total possibilities are there?
Solution
To solve this problem, we need to use the combination formula, which is used when the order of selection does not matter. The formula is:
C(n, k) = n! / [k!(n-k)!]
Where:
- n is the total number of items (in this case, 9 people)
- k is the number of items to choose (in this case, 3 players)
- "!" denotes a factorial, meaning the product of all positive integers up to that number.
Substituting these into the formula gives:
C(9, 3) = 9! / [3!(9-3)!] = 987 / (321) = 84
So there are 84 total possibilities for selecting 3 players from a group of 9 people.
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