Six-digit numbers are formed using the digits 1, 2, 3, 4, 5, and 6 without repetition. If all these numbers are arranged in strictly increasing order, then the position (rank) of the largest number in this sequence that is divisible by 4 is :

Step-by-step solution

To find the largest number divisible by 4 , we must maximize the leading digits while ensuring the last two digits form a multiple of 4 . Using the digits 1, 2, 3, 4, 5, 6 , we try to place the largest digits at the front: 6, 5, 4 . The remaining digits are 1, 2, 3 . For the number to be divisible by 4 , its last two digits must be a multiple of 4 . The possible multiples of 4 using 1, 2, 3 are 12 and 32 . To maximize the number, the hundreds digit should be as large as possible. If the last two digits are 12 , the