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

Step-by-step solution

Given, We have to form 6 digit number using the digits 4 ,   5   &   9 and for number should be divisible by 6 which means that the addition of number should be divisible by 3 and unit place should be even, so we will make following cases: Case 1 The number is 444444 which can be arranged in 1 way, Case 2 when the number is formed using the digits 4 , 4 , 4 , 5 , 9 and last place is fixed with 4 , that can be arranged in 5 ! 3 ! = 20   ways Case 3 when number is formed using the digits 4 , 4