Question

How many numbers divisible by $5$ and lying between $3000$ and $4000$ can be formed from the digits $3,4,5,6,7$ and $8$, no digit being repeated in any number?

Answer 1

$3,4,5,6,7,8$

The number is divisible by $5$ so the last digit can be $5$ one-ways

The number should be between $3000$ and $4000$ so the first digit can be $3$ in one-ways

Since repetition is not allowed second and third digit can be in $4$ and $3$ ways

so total ways $=1\times 4\times 3\times 1=12$