In how many ways can a committee of 2 women and 3 men be chosen from 6 men and 5 women?

Assessment: JAMB UTME - Mathematics - 2010 Subject: General Mathematics

Question 1 Report

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.

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