Question

How many numbers lying between $99\&1000$ be made from the digits $2,3,7,0,8,6$ when the digits occur only once in each number?

Answer 1

Finding the number of numbers lying between $99\&1000$ :

Given that the numbers are made from the digits $2,3,7,0,8,6$ only and the digits occur only once in each number.

Between $99\&1000$ there are all three digits numbers

We are given with $2,3,7,0,8,6$

$0$ cannot be taken for the hundreds place.

Therefore, hundreds place can be filled in $5$ ways, tens place in $5$ ways and once place in $4$ ways.

So, Total number of ways $=5x5x4=100$

Hence, the total numbers lying between $99\&1000$ that can be formed with $2,3,7,0,8,6$ digits are $100$.