The total number of 5 -digit numbers, formed using the digits 0, 1, 2, 3, 4 and 5 , without repetition, which are divisible by 4 , is equal to __________

Step-by-step solution

For a number to be divisible by 4 , the number formed by its last two digits must be divisible by 4 . Using the digits 0, 1, 2, 3, 4, 5 without repetition, the possible two-digit endings are 04, 12, 20, 24, 32, 40 and 52 . We can divide these into two cases: Case 1: The ending contains 0 (i.e., 04, 20, 40 ). There are 3 such endings. For each ending, the remaining 3 positions of the 5 -digit number must be filled using the remaining 4 digits. Since 0 is already used, there is no restriction on the first digit. Numb