Question

How many numbers between 2000 and 5000 can be made from the digits 1, 2, 4, 5, 7 and 8 if each digit is used only once?

Answer 1

We can have `120` such numbers.

Explanation:

As the number is between `2000` and `5000`, it means the digit in thousand's place is either `2` or `4`.

If digit in thousand place is `2`, we can have `1,4,5,7,8` in hundred's place, ten's place and unit's place. We can choose three digits out of five in `P_3^5=5xx4xx3=60` ways.

Similarly if digit in thousand place is `4`, we can have `1,2,5,7,8` in hundred's place, ten's place and unit's place and we can choose three digits out of five in `P_3^5=5xx4xx3=60` ways.

Hence, in all we can have `120` such numbers.