Question

The chess club at a private school has 15 boys and 8 girls. How many ways can a committee be selected consisting of 2 boys and 2 girls?

Answer 1

To find the number of ways a committee can be selected consisting of 2 boys and 2 girls from the chess club, use combinations. The number of ways to choose 2 boys out of 15 is C(15,2) and the number of ways to choose 2 girls out of 8 is C(8,2). Multiply these two combinations to get the total number of ways to select a committee with 2 boys and 2 girls.

Step-by-step explanation:

To find the number of ways a committee can be selected consisting of 2 boys and 2 girls from the chess club, we need to use combinations. The number of ways to choose 2 boys out of 15 is denoted as C(15,2) and the number of ways to choose 2 girls out of 8 is denoted as C(8,2). Multiplying these two combinations will give us the total number of ways to select a committee with 2 boys and 2 girls.

Using the formula for combinations, C(n,r) = n!/(r!(n-r)!), we can calculate:

C(15,2) = 15!/(2!(15-2)!) = 15!/(2!13!) = (15*14)/(2*1) = 105

C(8,2) = 8!/(2!(8-2)!) = 8!/(2!6!) = (8*7)/(2*1) = 28

So, the number of ways to select a committee consisting of 2 boys and 2 girls is 105 * 28 = 2,940.