Mathematics 2000 JAMB Past Questions - Question 49: In how many ways can a delegation of 3 be chosen from among 5 men and 3 women ,if at least one man and at least one woman must be included ?

Correct Answer

D

Explanation

To find the number of ways a delegation of 3 can be chosen from 5 men and 3 women, with the condition that at least one man and at least one woman must be included, we can use the principle of inclusion-exclusion.First, let's calculate the total number of ways to choose a delegation of 3 from the total pool of 8 people (5 men + 3 women):Total number of ways = C(8, 3) = 8! / (3! * (8-3)!) = 56Next, let's calculate the number of ways to choose a delegation of 3 that includes only men:Number of ways to choose 3 men from 5 men = C(5, 3) = 5! / (3! * (5-3)!) = 10Similarly, let's calculate the number of ways to choose a delegation of 3 that includes only women:Number of ways to choose 3 women from 3 women = C(3, 3) = 3! / (3! * (3-3)!) = 1Now, let's subtract the number of delegations that include only men or only women from the total number of ways to get the number of delegations that include at least one man and at least one woman:Number of ways to choose a delegation with at least one man and at least one woman = Total number of ways - Number of ways with only men - Number of ways with only women= 56 - 10 - 1= 45Therefore, there are 45 ways to choose a delegation of 3 from among 5 men and 3 women, with the condition that at least one man and at least one woman must be included.