Question

What is the number of $3$-digit number that can be formed using the digits $0$, $1$ and $5$, without repeating a digit in any number?

Answer 1

Number of $3$-digit number that can be formed using the digits $0$, $1$ and $5$, without repeating a digit in any number:

Step 1: If $0$ is at the hundred place:

It would result in two numbers i.e. $15$ and $51$. But these are $2$-digit number.

So, this case is not possible.

Step 2: If $1$ is at the hundred place:

It would result in two numbers i.e. $105$ and $150$.

So, two numbers can be formed in this case.

Step 3: If $5$ is at the hundred place:

It would result in two numbers i.e. $501$ and $510$.

So, two numbers can be formed in this case as well.

Thus, in total four $3$-digit number numbers can be formed using the digits $0$, $1$ and $5$, without repeating a digit in any number i.e. $105$, $150$, $501$ and $510$.