The number of integers greater than 6000 that are divisible by 4 , which can be formed using the digits 1, 2, 5, 6, 8 without repetition, is

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 1, 2, 5, 6, 8 without repetition, the possible valid two-digit endings are 12, 16, 28, 52, 56, and 68 (a total of 6 endings). The valid integers can be either 5 -digit or 4 -digit numbers. Case 1: 5 -digit numbers. Any 5 -digit number formed using these digits is greater than 6000 . For each of the 6 valid endings, the remaining 3 digits can be arranged in the first three places in 3! = 6 ways. Tot