The total number of three-digit numbers, divisible by 3 , which can be formed using the digits 1 , 3 , 5 , 8 , if repetition of digits is allowed, is

Step-by-step solution

Given, Three-digit number to be formed which are divisible by 3 using the digits 1 , 3 , 5 , 8 and repetition is allowed, Now taking case 1 , where all digits are same, we get 1 , 1 , 1 ,   3 , 3 , 3 ,   5 , 5 , 5 ,   8 , 8 , 8 → 4   ways Now taking case 2 , where 2 - digit are same and one is distinct, we get 5 , 5 , 8 → 3 ! 2 ! = 3   ways,   8 , 8 , 5 →   3   ways Now taking case 3 , where all are distinct, we get 1 , 3 , 5 → 6  ways ,   1