Final answer:
To find the total number of committees that can be formed from 9 men and 10 women, the number of combinations for selecting 4 men from 9 and 4 women from 10 must be calculated separately and then multiplied together. This results in a total of 26,460 different committees.
Step-by-step explanation:
To determine how many different committees can be formed, each consisting of 4 men and 4 women from a pool of 9 men and 10 women, we use combinations. We calculate the number of ways to choose 4 men from 9 and multiply it by the number of ways to choose 4 women from 10.
The number of ways to choose 4 men from 9 is given by the combination formula: 9C4 = 9! / (4!(9-4)!).
The number of ways to choose 4 women from 10 is given by the combination formula: 10C4 = 10! / (4!(10-4)!).
Multiplying these two values together gives the total number of different committees that can be formed:
(9C4) × (10C4) = (9! / (4!(9-4)!) × (10! / (4!(10-4)!)).
After calculating the factorials and simplifying, we can find the result for the total number of different committees. For instance:
9C4 = (9×8×7×6)/(4×3×2×1) = 126
10C4 = (10×9×8×7)/(4×3×2×1) = 210
Therefore, the total number of different committees is 126 × 210 = 26,460.