Question

In how many ways 5 men can draw water from 5 taps if no tap can be used more than once?

Answer 1

Hint:Here, use the concept of permutation as given that no tap can be used more than once, so repetition is not allowed. This is just like arranging 5 men in 5 places, so find the number of ways it can be done.

Complete step by step solution:
We have 5 men and 5 taps and no tap can be used more than once.
So, the first man can draw water from any of the 5 taps.
Second man can draw water from any of the remaining 4 taps.
Third man can draw water from any of the remaining 3 taps.
Fourth man can draw water from any of the remaining 2 taps.
Fifth man can draw water from the remaining 1 tap.
Hence the total number of ways 5 men can draw water from 5 tap = 5!
$ = 5 \times 4 \times 3 \times 2 \times 1 = 120$

$\therefore$ The number of ways 5 men can draw water from 5 taps if no tap can be used more than once is 120.

Note:
In this question we will keep in mind that no tap should be used more than once because this is the given condition in the above question. Every man has a different number of ways to draw water from tap and after using a tap by the first man then the number of ways decreases because the second man cannot use the tap which was already used by the first man. So, the second man has only 4 taps to use in which he can draw water from one of the remaining four taps. Similarly, the third man is left with only 3 taps in which he will also use one of the remaining 3 taps. In this way the last or fifth man will leave with only 1 tap which he will use to draw water. Then finally the answer will be the product of ways in which 5 men can draw water from 5 taps.