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?
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.
To form a committee of 6 with an equal number of boys and girls, we need to select 3 boys and 3 girls.
First, let's calculate the number of ways to choose 3 boys from a class of 14 boys. This can be done using the combination formula, which is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of options and r is the number of options to be chosen.
In this case, we have n = 14 (boys) and r = 3 (boys), so the calculation would be:
C(14, 3) = 14! / (3!(14-3)!) = (14 * 13 * 12) / (3 * 2 * 1) = 286.
So, there are 286 ways to choose 3 boys from a class of 14 boys.
Similarly, let's calculate the number of ways to choose 3 girls from a class of 9 girls:
C(9, 3) = 9! / (3!(9-3)!) = (9 * 8 * 7) / (3 * 2 * 1) = 84.
So, there are 84 ways to choose 3 girls from a class of 9 girls.
To find the total number of ways to choose an equal number of boys and girls, we multiply the number of ways to choose boys and the number of ways to choose girls:
Total number of ways = 286 * 84 = 24024.
Therefore, there are 24,024 ways to choose an equal number of boys and girls to form a committee of 6 to analyze classroom productivity.