Exact Science - Problem of The Day - 33 | Exact Science

33

N boys and N girls go out to dance. In how many ways can they all dance (boys must dance with girls)? 💃🏻 🕺🏻

Answer

N!

SOLUTIOn

1st boy has N possibilities for choosing a girl, then

2nd boy has N-1 possibilities for choosing a girl, then

...

nth boy has just 1 girl left to dance with.

Seemingly there are N(N−1)(N−2)...1=N! possible combinations.

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