How many ways can a committee of 7 be selected from a club with 15 members?

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Step:1 ：We are given a club with 15 members and we are asked to find out how many ways a committee of 7 can be selected.Step:2 ：This is a problem of combinations, where order does not matter. The formula for combinations is given by ( C(n, k) = frac{n!}{k!(n-k)!} ), where ( n ) is the total number of items, ( k ) is the number of items to choose, and ( ! ) denotes factorial.Step:3 ：Substituting the given values into the formula, we get ( C(15, 7) = frac{15!}{7!(15-7)!} ).Step:4 ：Calculating the factorials and simplifying the expression, we find that there are (boxed{6435}) ways to select a committee of 7 from a club with 15 members.

Answer

Step: 1 ：We are given a club with 15 members and we are asked to find out how many ways a committee of 7 can be selected.Step: 2 ：This is a problem of combinations, where order does not matter. The formula for combinations is given by ( C(n, k) = frac{n!}{k!(n-k)!} ), where ( n ) is the total number of items, ( k ) is the number of items to choose, and ( ! ) denotes factorial.Step: 3 ：Substituting the given values into the formula, we get ( C(15, 7) = frac{15!}{7!(15-7)!} ).Step: 4 ：Calculating the factorials and simplifying the expression, we find that there are (boxed{6435}) ways to select a committee of 7 from a club with 15 members.

How many ways can a committee of 7 be selected from a club with 15 members?

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