Final answer:
A committee of 3 men and 4 women can be formed in 2450 different ways from a group of 7 men and 8 women by calculating the combinations separately for men and women, then multiplying the results.
Step-by-step explanation:
To determine how many ways a committee can be formed from a group of 7 men and 8 women when the committee is to be made up of 3 men and 4 women, one would use combinations as this is a problem of combinatorics. We are combining different groups without regard to the order in which the committee members are selected.
First, calculate the number of ways to choose the men:
There are 7 men and 3 spots on the committee for them, so we calculate this as 7 choose 3, which is C(7,3) or 35 ways.
Next, calculate the number of ways to choose the women:
There are 8 women and 4 spots on the committee for them, so we calculate this as 8 choose 4, which is C(8,4) or 70 ways.
Finally, multiply the number of ways to choose the men by the number of ways to choose the women to find the total number of ways to form the committee:
35 ways to choose men × 70 ways to choose women = 2450 ways to form the committee.