Mathematics Question on permutations and combinations

Question

The total number of six digit numbers, formed using the digits $4,5,9$ only and divisible by 6 , is __

Accepted Answer

The correct answer is 81

4,5,9,4,4,4⇒3!5!=20
4,5,9,5,5,5⇒4!5!=5
4,5,9,9,9,9⇒4!5!=5
4,5,9,4,5,9⇒2!2!5!=30
Total =81