In a committee of 5, which must be selected from 4 males and 3 females. In how many ways can the members be chosen if it were to include 2 females?

In a committee of 5, which must be selected from 4 males and 3 females. In how many ways can the members be chosen if it were to include 2 females?

Answer Details

To select a committee of 5 members, including 2 females, we can break down the problem into the following steps: Step 1: Select 2 females from the 3 available females. This can be done in $\binom{3}{2} = 3$ ways. Here, $\binom{n}{r}$ denotes the number of ways to choose r items from a set of n items, also known as "n choose r". Step 2: Select 3 members from the remaining 4 males and 1 female. This can be done in $\binom{4}{3} \cdot \binom{1}{0} = 4$ ways. Here, we choose 3 males from the 4 available males, and 0 females from the 1 remaining female. Step 3: Multiply the results of Steps 1 and 2 to obtain the total number of ways to choose the committee. Therefore, the total number of ways to select a committee of 5 members, including 2 females, is: $\binom{3}{2} \cdot \binom{4}{3} \cdot \binom{1}{0} = 3 \cdot 4 \cdot 1 = 12$ Hence, there are 12 ways to choose the members of the committee. Therefore, the answer is 12 ways.