Question

question
if the math olympiad club consists of 11 students, how many different teams of 3 students can be formed for competitions?

answer attempt 1 out of 2

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Explanation:

Step1: Identify the problem type

This is a combination problem since the order of students in the team does not matter. The formula for combinations is \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 11 \) (total number of students) and \( k = 3 \) (number of students per team).

Step2: Calculate factorial values

First, calculate the factorials:

• \( n!=11!=11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1 \)
• \( k!=3!=3\times2\times1 = 6 \)
• \( (n - k)!=(11 - 3)!=8!=8\times7\times6\times5\times4\times3\times2\times1 \)

Step3: Substitute into the combination formula

Substitute \( n = 11 \) and \( k = 3 \) into \( C(n, k) \):

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Answer:

165