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.