Final answer:
To form a team of 2 men and 3 women from a group of 5 men and 7 women, you can use the concept of combinations. The number of ways to choose 2 men from a group of 5 men is given by the combination formula C(5,2). Similarly, the number of ways to choose 3 women from a group of 7 women is given by the combination formula C(7,3). The total number of ways to form the team is found by multiplying the two combinations together: C(5,2) * C(7,3) = 350.
Step-by-step explanation:
To form a team of 2 men and 3 women from a group of 5 men and 7 women, you can use the concept of combinations. The number of ways to choose 2 men from a group of 5 men is given by the combination formula C(5,2). Similarly, the number of ways to choose 3 women from a group of 7 women is given by the combination formula C(7,3). To find the total number of ways to form the team, you can multiply the two combinations together: C(5,2) * C(7,3).
Using the formula for combinations, the calculation is as follows:
C(5,2) = 5! / (2! * (5-2)!) = 10
C(7,3) = 7! / (3! * (7-3)!) = 35
The total number of ways to form the team is: C(5,2) * C(7,3) = 10 * 35 = 350.
Therefore, the correct answer is C. 350.