A group consists of 5 boys and 6 girls how many committees of five can be formed that consists of 2 boys and 3 girls?

combination of

5! divided by 2!3!

combination of
6! divided by 3!3!

factorial means 5! = 5x4x3x2x1

Multiply both of your answers together to get the number of committees.

To determine the number of committees that can be formed, we need to calculate the combination of boys and girls that can be selected.

Step 1: Calculate the number of ways to select 2 boys from a group of 5.
- This can be calculated using the combination formula: nCr = n! / (r!(n - r)!), where n is the total number of elements and r is the number of elements to be selected.
- In this case, we have 5 boys and need to select 2, so the calculation becomes: 5C2 = 5! / (2! * (5 - 2)!) = (5 * 4) / (2 * 1) = 10.

Step 2: Calculate the number of ways to select 3 girls from a group of 6.
- Using the same combination formula: 6C3 = 6! / (3! * (6 - 3)!) = (6 * 5 * 4) / (3 * 2 * 1) = 20.

Step 3: Multiply the results obtained from Step 1 and Step 2 to find the total number of committees.
- The number of committees can be determined by multiplying the number of ways to select boys and the number of ways to select girls: 10 * 20 = 200.

Therefore, there can be 200 committees formed consisting of 2 boys and 3 girls.

To determine the number of committees that can be formed with 2 boys and 3 girls from a group consisting of 5 boys and 6 girls, you can use combinations.

First, calculate the number of ways to select 2 boys from a group of 5 boys. This can be done using the combination formula:

C(n, r) = n! / (r!(n-r)!)

Where n is the total number of elements and r is the number of elements to be selected.

In this case, calculating the number of ways to select 2 boys from 5 boys:

C(5, 2) = 5! / (2!(5-2)!)
= 5! / (2!3!)
= (5 * 4 * 3!) / (2! * 3!)
= (5 * 4) / (2!)
= 10

So, there are 10 ways to select 2 boys from a group of 5 boys.

Next, calculate the number of ways to select 3 girls from a group of 6 girls. Using the same combination formula:

C(6, 3) = 6! / (3!(6-3)!)
= 6! / (3!3!)
= (6 * 5 * 4!) / (3! * 2!)
= (6 * 5) / (2!)
= 15

So, there are 15 ways to select 3 girls from a group of 6 girls.

Finally, multiply the two results together to find the total number of committees:

Total number of committees = Number of ways to select 2 boys * Number of ways to select 3 girls
= 10 * 15
= 150

Therefore, there are 150 different committees that can be formed with 2 boys and 3 girls from the given group.