In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?Choices:- 266 5040 11760 86400

The problem can be solved using the concept of combinations in statistics.

Step 1: We need to 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 items, r is the number of items to choose, 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 need to select 6 women out of 10. Using the same combination formula, the number of ways to do this is C(10, 6) = 10! / [(10-6)!6!] = 210.

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 form the committee.

So, the total number of ways = 56 * 210 = 11760.

Therefore, the correct answer is 11760.

The problem can be solved using the concept of combinations in probability.

First, we need to 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 items, r is the number of items to choose, and '!' denotes factorial.

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

Next, we need to select 6 women out of 10. Using the same formula, the number of ways to do this is C(10, 6) = 10! / [(10-6)!6!] = 210.

Since these are independent events, we multiply the number of ways to get the total number of ways to form the committee.

So, the total number of ways = 56 * 210 = 11760.

Therefore, the answer is 11760.