The total number of 5 -digit numbers, formed by using the digits 1 , 2 , 3 , 5 , 6 , 7 without repetition, which are multiple of 6 , is

Step-by-step solution

Given set 1 , 2 , 3 , 5 , 6 , 7 Here sum is 1 + 2 + 3 + 5 + 6 + 7 = 24 So there will be two cases Case (i) When numbers are 1 , 2 , 5 , 6 , 7 Arrangement will be _   _   _   _   2   &   _   _   _   _   6 In unit place 2 & 6 can take place because for multiple of 6 number should be even & sum of digits should be multiple of 3 . So total way in which remaining number can be taken will be 4 ! × 2 = 48 ways Case (ii) When numbers are 1 , 2 , 3 , 5 , 7 Arrangeme