What is the number of 6 digit numbers that can be formed only by using 0,1,2,3,4 and 5 (each once); and divisible by 6 ?

Step-by-step solution

Sum of digits =0+1+2+3+4+5=15 All numbers are divisible by 3 . To make it divisible by 6 , it must be divisible by 2 i.e. even number at unit place. Case 1 : When 0 is at unit place Number of numbers =5!=120 Case 2: 2,4 at unit place Number of numbers =4! 4 2=192 Total numbers =120+192=312 .