Total numbers of 3 -digit numbers that are divisible by 6 and can be formed by using the digits 1 , 2 , 3 , 4 , 5 with repetition, is ________

Step-by-step solution

A number is divisible by 6 when it is divisible by 2 and 3 both. The three digit number can be a ¯ b ¯ 2 ¯ . a + b can be 4 , 7 , 10 If a + b = 4 then ( a ,   b ) can be ( 1 , 3 ) , ( 3 , 1 ) , ( 2 , 2 ) If a + b = 7 then ( a ,   b ) can be ( 2 , 5 ) , ( 5 , 2 ) , ( 3 , 4 ) , ( 4 , 3 ) If a + b = 10 then ( a ,   b ) can be ( 5 , 5 ) So, 8 such cases when 2 is at unit's place Similarly, there exist 8 such cases when 4 is at unit's place. Total = 16 cases. Hence this is the requi