If a teacher wants to choose 3 students as a group to participate in a math exam, the total number of students in the class is 10, how many options for the teacher?
Question
If a teacher wants to choose 3 students as a group to participate in a math exam, the total number of students in the class is 10, how many options for the teacher?
Solution
This is a combination problem. The number of ways to choose k items from a group of n items is given by the combination formula:
C(n, k) = n! / [k!(n-k)!]
where:
- n is the total number of items
- k is the number of items to choose
- "!" denotes factorial, which is the product of all positive integers up to that number
We need to choose 3 students out of 10. So, we calculate the number of combinations:
C(10, 3) = 10! / [3!(10-3)!] = 120
So, there are 120 options for the teacher.
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