Final answer:
The detailed answer explains how to calculate the number of committees of 3 men and 4 women that can be formed from a given group of men and women using combination formulas.
Explanation:
Calculating the number of committees:
To find the number of committees of 3 men and 4 women that can be formed from 8 men and 6 women, you can use combination formulas.
The formula for combinations: C(n, k) = n! / (k!(n-k)!).
- Number of ways to choose 3 men out of 8: C(8, 3).
- Number of ways to choose 4 women out of 6: C(6, 4).
- To find total committees, multiply the results above: Total committees = C(8, 3) C(6, 4).
Applying the formula:
C(8, 3) = 8! / (3!(8-3)!) = 56;
C(6, 4) = 6! / (4!(6-4)!) = 15;
Total committees = 56 15 = 840 ways.
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