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:
$=12$
$4 \times 3$
$12 \rightarrow 3,4,5 \rightarrow 3 !=6$
$15 \rightarrow 2,3,4 \rightarrow 3 !=6$
$24 \rightarrow 1,3,5 \rightarrow 3 !=6$
$42 \rightarrow 1,2,3 \rightarrow 3 !=6$
Required No. $=24+12-4=32$