The number of 5 digited numbers that can be formed using the digits 0, 1, 2, 3, 4, 5 that are divisible by 6 when repetition is not allowed is

Given digits 0, 1, 2, 3, 4, 5

A number is divisible by 6 if it is divisible by 2 and 3

The possible 5 digits to make it divisible by 3 are 0, 1, 2, 4, 5 (or)

1, 2, 3, 4, 5

The number of 5 digit numbers that are, formed by 0, 1, 2, 4, 5 and divisible by 2 are $=3\times 3!+3\times 3!+4!$

$=18+18+24$

$=60$

The number of 5 digit numbers that are formed by 1, 2, 3, 4, 5 and divisible by 2 are $=2\times 4!$

$=48$

$\therefore$  Required number of ways $=60+48$

$=108$