A dance class consists of 22 students, of which 10 are women and 12 are men. If 5 men and 5 women are to be chosen and then paired off, how many results are possible?

# A dance class consists of 22 students, of which 10 are women and 12 are men. If 5 men and 5 women are to be chosen and then paired off, how many results are possible?

J
240 points

A dance class consists of 22 students, of which 10 are women and 12 are men. If 5 men and 5 women are to be chosen and then paired off, how many results are possible?

probability

8.7k points

Pick 5 men from the 12 possible where the order doesn't matter. And pick 5 women from the 10 possible where the order doesn't matter. After we've got the men and women we pair them off in 5! possible ways.

$$\begin{pmatrix} 12 \\ 5 \end{pmatrix} \cdot \begin{pmatrix} 10 \\ 5 \end{pmatrix} \cdot 5!=792 \cdot 252 \cdot 120 = 23950080$$

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