From a class of 5 girls and 7 boys, a committee consisting of 2 girls and 3 boys is to be formed. How many ways can this be done?

Answer Details

To find the number of ways to form a committee consisting of 2 girls and 3 boys from a group of 5 girls and 7 boys, we need to use the concept of combinations. Combinations allow us to determine how many ways we can choose a subset of items from a larger set, without regard to the order of selection.

First, we calculate the number of ways to choose 2 girls out of 5. This is done using the combination formula:

Combination Formula: nCr = ^n! / (r! * (n-r)!)

Here, n is the total number of items to choose from, and r is the number of items to choose.

Choosing 2 girls out of 5:

5C2 = ^5! / (2! * (5-2)!) = (5 * 4) / (2 * 1) = 10

So, there are 10 ways to choose 2 girls from a group of 5 girls.

Next, we calculate the number of ways to choose 3 boys out of 7:

Choosing 3 boys out of 7:

7C3 = ^7! / (3! * (7-3)!) = (7 * 6 * 5) / (3 * 2 * 1) = 35

So, there are 35 ways to choose 3 boys from a group of 7 boys.

To find the total number of ways to form the committee, we multiply the number of ways to choose the girls by the number of ways to choose the boys:

Total number of ways: 10 * 35 = 350

Thus, there are 350 ways to form the committee consisting of 2 girls and 3 boys from the given class. Therefore, the answer is 350 ways.