Question

In how many ways can $6$ women draw water from $6$ wells, if no well remains used?

Answer 1

$6$ women $⟶6$ wells

Each women goes to each well

Number of ways each women can draw

${}^6{P}_6\Rightarrow \frac{6!}{(6-6)!}\Rightarrow \frac{6!}{0!}\Rightarrow 6\times 5\times 4\times 3\times 2\times 1\Rightarrow 30\times 12\times 2\Rightarrow 720$

Therefore there are $720$ ways