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?

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Ok, so far I have 10C5 and 12C5, have no clue what to do next.

multiply them
then multiply by 5!

why though? 5! is the permutation of 5 pairs... but why multiply men and women?

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