There are twelve students in a group, they want to choose three people at random for the speech contest, how many different three-people groups are possible?
Question
There are twelve students in a group, they want to choose three people at random for the speech contest, how many different three-people groups are possible?
Solution
The number of ways to select three students from twelve is a combination problem.
In mathematics, a combination is a selection of items without regard to the order. The formula for combinations is:
C(n, k) = n! / [k!(n-k)!]
where: n is the total number of items, k is the number of items to select, "!" denotes factorial, which is the product of all positive integers up to that number.
Substituting the given values into the formula, we get:
C(12, 3) = 12! / [3!(12-3)!]
= 12! / [3! * 9!]
= (12 * 11 * 10) / (3 * 2 * 1)
= 220
So, there are 220 different three-people groups possible from twelve students.
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