Two groups

The group of 10 girls should be divided into two groups with at least 4 girls in each group. How many ways can this be done?

Correct answer:

n =  462

Step-by-step explanation:

$$\begin{gathered} C_4(10)=\left({\displaystyle \genfrac{}{}{0px}{}{10}{4}}\right)={\displaystyle \frac{10!}{4!(10-4)!}}={\displaystyle \frac{10\cdot 9\cdot 8\cdot 7}{4\cdot 3\cdot 2\cdot 1}}=210 \\ {C}_5(10)=\left({\displaystyle \genfrac{}{}{0px}{}{10}{5}}\right)={\displaystyle \frac{10!}{5!(10-5)!}}={\displaystyle \frac{10\cdot 9\cdot 8\cdot 7\cdot 6}{5\cdot 4\cdot 3\cdot 2\cdot 1}}=252 \\ n=\left(\genfrac{}{}{0px}{}{10}{4}\right)+\left(\genfrac{}{}{0px}{}{10}{5}\right)=462 \end{gathered}$$

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