n how many different ways a group of 5 men and 7 women can be formed out of 8 men and 10 women?Choices:- 4240 6380 6720 5614

The problem involves combinations.

Step 1: We first select 5 men out of 8. The number of ways to do this is given by the combination formula C(n, r) = n! / [(n-r)!r!], where n is the total number of options, r is the number of options chosen, and '!' denotes factorial.

So, the number of ways to select 5 men out of 8 is C(8, 5) = 8! / [(8-5)!5!] = 56.

Step 2: We then select 7 women out of 10. Using the same formula, the number of ways to do this is C(10, 7) = 10! / [(10-7)!7!] = 120.

Step 3: Since the selections of men and women are independent events, we multiply the number of ways to get the total number of ways to select the group.

So, the total number of ways = 56 * 120 = 6720.

Therefore, the answer is 6720.