Final answer:
To form a committee of four men and three women from ten men and six women, calculate the combinations for each gender separately and multiply the results: there are 210 ways to select men and 20 ways to select women, giving a total of 4200 ways to form the committee.
Step-by-step explanation:
To determine the number of ways a committee of four men and three women can be formed from a group of ten men and six women, you need to calculate the combinations separately for men and women and then multiply the two results. For the men, there are C(10, 4) ways to choose four men from ten. This is calculated using the combination formula C(n, k) = n! / (k!(n - k)!), which gives us C(10, 4) = 10! / (4!(10 - 4)!) = 210 ways. For the women, there are C(6, 3) ways to choose three women from six. Using the same formula, we get C(6, 3) = 6! / (3!(6 - 3)!) = 20 ways. To find the total number of ways to form the committee, we multiply the number of ways to select the men by the number of ways to select the women: 210 ways to select men × 20 ways to select women = 4200 ways to form the committee.