Question

A $5digit$ number divisible by $3$ is to be formed using the digits $0,1,2,3,4$ and $5$ without repetition. Find total number of such numbers.

Answer 1

$1+2+3+4+5=15$ is divisible by 3

The number of way in which five number are formed $=5!$ way

$\Rightarrow 120$ ways

The five digit number that can be formed using $0,1,2,3,4$ are

first digit $=4$ ways

second digit $=4$ ways

third digit $3$ ways

fourth digit $2$ ways

fifth digit $1$ way

Total number of ways $=4\times 4\times 3\times 2\times 1$

$\Rightarrow 4\times 4!$

$\Rightarrow 96$

Hence,

Total number of ways $=120+96$

$\Rightarrow 216$