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

1.	In how many ways can 6 women draw water from 6 wells if no well remains unused?
Answer» 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 2nd well and so on. Lastly, there will be single women left to draw water from the 6th 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) = \(\frac{6!}{(6-6)!}\) = \(\frac{6!}{0!}\) = \(\frac{720}{1}\) Hence, this can be done in 720 ways.

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

Answer»

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 2nd well and so on. Lastly, there will be single women left to draw water from the 6th 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) = \(\frac{6!}{(6-6)!}\)

= \(\frac{6!}{0!}\) = \(\frac{720}{1}\)

Hence, this can be done in 720 ways.