How many ways can a committee of 4 be selected from a club with 12 members?

Solution:

We can use the combination formula to select a committee of 4 members from a club with 12 members.

Combination formula is given by \(^{n}C_{r}=\frac{n!}{r!(n-r)!)}\)

Heren n = 12, r =4

So, \(^{12}C_{4}=\frac{12!}{4!(12-4)!)}\)

\(^{12}C_{4}=\frac{12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{(4\times 3\times 2\times 1)(8)!}\)

= \(^{12}C_{4}=\frac{12\times 11\times 10\times 9}{(4\times 3\times 2\times 1)}\)

= \(^{12}C_{4}=\frac{11880}{24}\)

= \(^{12}C_{4}=495\)

Therefore, \(^{12}C_{4}=495\)

How many ways can a committee of 4 be selected from a club with 12 members?

Summary:

495 ways a committee of 4 can be selected from a club with 12 members.