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

A number is divisible by 6 of sum of digits is a multiple of 3 and number is an even number.

(I).  5 digit even Numbers formed using 1, 2, 3, 4, 5     

       units place can be filled by using 2, 4 in 2 ways.     

       Remaining 4 digits can be filled in 4! Ways No. of 5 digit no’s divisible by 6=2(4!) =48

(II).  5 digit even no’s using 0, 1, 2, 4, 5. 

       Case I :  5 digit Numbers ending with 0=4!=24

       Case II : 5 digit Numbers ending with 2, 4=2(3(3!))=36    

                      Total no. of 5 digit Numbers  = 48+36+24=108

                            Divisible by 6           “