Question

How many different $3-$digit numbers can be formed by using the digits $0,2,$ and $5$ without repeating any digit in the number

Answer 1

Forming $3-$digit number using the given digits:

Arrange the given digits in descending order for the largest number

$5>2>0$
The greatest number is $520$

Arrange the given digits in ascending order for the smallest number

$0<2<5$

Since the smallest value digit is zero, place them in the second leftmost position.
Therefore, the smallest number is $205$

Interchange the digits in order to get numbers other than the greatest and smallest number.

New numbers when interchanging are $502,250$

Therefore, a total of four $3-$digit numbers are possible from the given set of digits.