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

$12\to 3,4,5\to 3!=6$
$15\to 2,3,4\to 3!=6$
$24\to 1,3,5\to 3!=6$
$45\to 1,2,3\to 3!=6$
total $=24$

divisible by $5$

$=4\times 3=12$

divisible by $\to 15$
$135;315;345;435$
$4$ numbers
Required Numbers $=24+12-4=32$