Question

The total number of numbers, lying between $100$ and $1000$ that can be formed with the digits $1,2,3,4,5$, if the repetition of digits is not allowed and numbers are divisible by either $3$ or $5$ is

Answer 1

Find the total number of numbers

Given : The numbers are either divisible by $3$ or $5$.

We need three digit number with the digits $1,2,3,4,5$.

Since $1+2+3+4+5=15$

So number of possible triplets of $15$ is $1\times 2\times 2$.

Therefore total numbers $=\left(4\times 3!\right)+\left(4\times 3\right)-\left(1\times 2\times 2!\right)$

$$\begin{gathered} =36-4 \\ =32 \end{gathered}$$

Hence total number of numbers, lying between $100$ and $1000$ that can be formed with the digits $1,2,3,4,5$, if the repetition of digits is not allowed and numbers are divisible by either $3$ or $5$ is $32$.