From a class of 14 boys and 9 girls, how many can i choose an equal number of boys and girls to form a committee of 6 to analyze classroom productivity?

Answer 1

To form a committee with an equal number of boys and girls, you can choose either 3 boys and 3 girls or 4 boys and 4 girls.

Option 1: Choosing 3 boys and 3 girls
Number of ways to choose 3 boys out of 14 boys: C(14, 3) = 14! / (3! * (14-3)!) = 364
Number of ways to choose 3 girls out of 9 girls: C(9, 3) = 9! / (3! * (9-3)!) = 84
Total number of ways to choose an equal number of boys and girls: 364 * 84 = 30,576

Option 2: Choosing 4 boys and 4 girls
Number of ways to choose 4 boys out of 14 boys: C(14, 4) = 14! / (4! * (14-4)!) = 1001
Number of ways to choose 4 girls out of 9 girls: C(9, 4) = 9! / (4! * (9-4)!) = 126
Total number of ways to choose an equal number of boys and girls: 1001 * 126 = 126,126

Therefore, you can choose an equal number of boys and girls to form a committee of 6 to analyze classroom productivity in 30,576 + 126,126 = 156,702 ways.