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_______.
Solution:
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. $=4 \times\lfloor 3+4 \times 3-1 \times 2 \times\lfloor 2=32$