In how many ways can 6 women draw water from 6 wells if no well remains

To find: number of arrangements of 6 women drawing water from 6 wells

Here, 6 wells are needed to be used by 6 women.

Therefore any one of the 6 women can draw water from the 1 well.

Similarly, any 5 women can draw water from the $2^{\text {nd }}$ well and so on.

Lastly, there will be single women left to draw water from the $6^{\text {th }}$ well.

Formula:

Number of permutations of $n$ distinct objects among $r$ different places, where repetition is not allowed, is

$P(n, r)=n ! /(n-r) !$

Therefore, permutation of 6 different objects in 6 places is

$P(6,6)=\frac{6 !}{(6-6) !}$

$=\frac{6 !}{0 !}=\frac{720}{1}=720$

Hence, this can be done in 720 ways.