Question

In how many ways can 4 women draw water from 4 taps, if no tap remains unused?

Answer 1

In this problem, we have to find out how many ways 4 women can draw water from 4 taps, if no tap remains unused. We can solve this problem by finding the number of options for each lady differently and we can multiply them. We should also remember that if one tap is assigned to one lady it cannot be used by another. We can now find the answer.

Complete step by step answer:
Here we have to find out how many ways 4 women can draw water from 4 taps, if no tap remains unused.
Here we have 5 different taps and five ladies.
When the first lady comes to draw the water from the tap, she will have five taps to choose.
Now if the second lady comes to draw water, she will have 4 taps to choose as one tap is already chosen.
Similarly, the third lady will have three options to choose from, the fourth lady will have 2 options and the fifth lady will have 1 option.
We can come to know that, the required number of ways to draw the water from the tap is,
$\Rightarrow 4\times 3\times 2\times 1=24$
Therefore, there are 24 ways, 4 women draw water from 4 taps, if no tap remains unused.

Note: We can also solve this problem using the permutation formula.
Where there are n ways to choose or the chosen number of ways.
${{\Rightarrow }^{n}}{{P}_{r}}=\dfrac{n!}{\left( n-r \right)!}$
We can now substitute the values, we get
${{\Rightarrow }^{4}}{{P}_{4}}=\dfrac{4!}{\left( 4-4 \right)!}=24$
Therefore, there are 24 ways, 4 women draw water from 4 taps, if no tap remains unused.