In how many ways can a committee of 2 women and 3 men be chosen from 6 men and 5 women?
Answer Details
To determine how many ways a committee of 2 women and 3 men can be chosen from 6 men and 5 women, we can use the combination formula. The number of combinations of k objects that can be chosen from a set of n objects is given by:
nCk = n! / (k! * (n - k)!)
where n! denotes n factorial, which is the product of all positive integers up to n.
So, in this case, the number of ways to choose 2 women from 5 is 5C2 = 5! / (2! * (5-2)!) = 10.
Similarly, the number of ways to choose 3 men from 6 is 6C3 = 6! / (3! * (6-3)!) = 20.
Using the multiplication principle, we can multiply these two numbers together to find the total number of ways to choose 2 women and 3 men:
10 * 20 = 200.
Therefore, there are 200 ways to choose a committee of 2 women and 3 men from 6 men and 5 women. The answer is (B) 200.