Commitee

A class consists of 12 males and 15 females. How many committees of 6 are possible if the committee must consist of 4 males and 2 females?

Final Answer:

x =  51975

Step-by-step explanation:

$$\begin{gathered} C_4(12)=\left(\genfrac{}{}{0ex}{}{12}{4}\right)=\frac{12!}{4!(12-4)!}=\frac{12\cdot 11\cdot 10\cdot 9}{4\cdot 3\cdot 2\cdot 1}=495 \\ {C}_2(15)=\left(\genfrac{}{}{0ex}{}{15}{2}\right)=\frac{15!}{2!(15-2)!}=\frac{15\cdot 14}{2\cdot 1}=105 \\ x=\left(\genfrac{}{}{0ex}{}{12}{4}\right)\cdot \left(\genfrac{}{}{0ex}{}{15}{2}\right)=495\cdot 105=51975 \end{gathered}$$

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