Final answer:
To find the number of ways to form a committee of three men from seven and two women from five, we calculate the combinations separately (7C3 for men and 5C2 for women) and multiply them together, resulting in 350 possible ways.
Step-by-step explanation:
The number of ways to choose a committee of three men from seven men and two women from five women can be calculated using the combination formula. For the men, we use the combination formula which is 7C3 (the number of ways to choose 3 from 7), and for the women, it's 5C2 (the number of ways to choose 2 from 5).
The formula for combinations is given by C(n, k) = n! / (k! * (n - k)!), where n is the total number of items to choose from, k is the number of items to choose, and '!' denotes factorial.
Using the formula, we get 7C3 = 7! / (3! * (7 - 3)!) = 35 and 5C2 = 5! / (2! * (5 - 2)!) = 10. To find the total number of ways to form the committee, we multiply these two results together: 35 * 10 = 350.
Therefore, the number of ways in which a committee consisting of three men and two women be chosen from seven men and five women is 350.