The problem
We need to determine the number of different committees that can be formed, where each committee consists of 3 girls and 2 boys, given that there are 7 girls and 5 boys to choose from.

Solution
To solve this problem, we can use combinations. A combination is a selection of items from a larger set without regard to the order of the items. In this case, we want to select 3 girls from 7 and 2 boys from 5.

Combining girls and boys
To find the number of different committees, we need to find the combination of girls and boys separately and then multiply them together.

Combining girls
To select 3 girls from a set of 7, we can use the combination formula, given by:

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

Where n is the total number of items in the set and r is the number of items to be selected.

Using this formula, we can calculate the number of ways to select 3 girls from 7:

C(7, 3) = 7! / (3!(7-3)!) = 7! / (3!4!) = (7 * 6 * 5) / (3 * 2 * 1) = 35

So, there are 35 different ways to select 3 girls from the set of 7.

Combining boys
Similarly, we need to find the number of ways to select 2 boys from a set of 5. Using the combination formula again:

C(5, 2) = 5! / (2!(5-2)!) = 5! / (2!3!) = (5 * 4) / (2 * 1) = 10

So, there are 10 different ways to select 2 boys from the set of 5.

Combining girls and boys
To find the total number of different committees, we need to multiply the number of ways to select girls and boys together:

Total number of different committees = 35 * 10 = 350

Therefore, there are 350 different committees that can be chosen from 7 girls and 5 boys, where each committee consists of 3 girls and 2 boys.