In how many ways 4 women draw water from 4 taps, if no tap remains unu

1.	In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Answer» 1^stwoman can draw water from anyone of the 4 taps. Now, as, it is given, that, No tap should remain unused So, 2^ndwoman can draw water from any of the remaining 3 taps. Similarly, 3^rd women can draw water from any of the remaining 2 taps. And, 4^th woman have to draw water from the remaining 1 tap. As, The operations are dependent, So, Total number of ways = 4\(\times\)3\(\times\)2\(\times\)1 = 4! Alternative Approach : The number of permutations of 4 objects taken 4 at a time is = ⁴P₄ = 4!.

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

Answer»

1^stwoman can draw water from anyone of the 4 taps.

Now, as, it is given, that,

No tap should remain unused

So,

2^ndwoman can draw water from any of the remaining 3 taps.

Similarly,

3^rd women can draw water from any of the remaining 2 taps.

And,

4^th woman have to draw water from the remaining 1 tap.

As,

The operations are dependent,

So,

Total number of ways = 4\(\times\)3\(\times\)2\(\times\)1

= 4!

Alternative Approach :

The number of permutations of 4 objects taken 4 at a time is = ⁴P₄

= 4!.