Question

Out of 8 boys and 10 girls, how many groups of 5 boys and 6 girls can be formed?

Answer 1

The total number of groups of 5 boys and 6 girls that can be formed is 11,760.

Step-by-step explanation:

To find the number of groups of 5 boys and 6 girls that can be formed, we can use the concept of combinations. The number of ways to choose 5 boys out of 8 is denoted by C(8, 5) and the number of ways to choose 6 girls out of 10 is denoted by C(10, 6).

So, the total number of groups of 5 boys and 6 girls that can be formed is equal to C(8, 5) * C(10, 6).

Using the formula for combinations, C(n, r) = n! / (r! * (n-r)!), we can calculate the values:

C(8, 5) = 8! / (5! * (8-5)!) = 56

C(10, 6) = 10! / (6! * (10-6)!) = 210

Therefore, the total number of groups that can be formed is 56 * 210 = 11,760.