Competition

Fifteen boys and ten girls are in the class. In the school competition, a six-member team composed of four boys and two girls is selected. How many ways can we choose students?

Correct answer:

n =  61425

Step-by-step explanation:

$$\begin{gathered} C_4(15)=\left(\genfrac{}{}{0ex}{}{15}{4}\right)=\frac{15!}{4!(15-4)!}=\frac{15\cdot 14\cdot 13\cdot 12}{4\cdot 3\cdot 2\cdot 1}=1365 \\ {C}_2(10)=\left(\genfrac{}{}{0ex}{}{10}{2}\right)=\frac{10!}{2!(10-2)!}=\frac{10\cdot 9}{2\cdot 1}=45 \\ n=\left(\genfrac{}{}{0ex}{}{15}{4}\right)\cdot \left(\genfrac{}{}{0ex}{}{10}{2}\right)=1365\cdot 45=61425 \end{gathered}$$

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