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

We need three digits numbers.
Since $1+2+3+4+5=15$
So, number of possible triplets for multiple of $15$ is $1 \times 2 \times 2$
so Ans. $=4 \times 3+4 \times 3-1 \times 2 \times 2=32$