Select four executives from 15 executives to participate in this year's summary meeting. How many choices are there?
Question
Select four executives from 15 executives to participate in this year's summary meeting. How many choices 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, 15 executives)
- k is the number of items to choose (in this case, 4 executives)
- "!" denotes a factorial, meaning the product of all positive integers up to that number.
Substituting these into the formula gives:
C(15, 4) = 15! / [4!(15-4)!] = (15141312) / (4321) = 1365
So there are 1365 different ways to select four executives from a group of 15 executives.
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