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# How Many 5 Digit Numbers Can Be Formed Using the Digits 1, 2, 3, 4, 5 (But With Repetition) that are Divisible by 4?

TopPermutation is a mathematical method which can be used to tell us different possible ways in which items or Numbers can be arranged. In Combination order does not matter, but it is not the case with permutations. For example, if some students have to be seated according to their increasing ages, it would matter in case of Permutation to maintain this order. While making permutations you need to be sure about repetition, whether it is to be considered or not in our calculations. For example if we consider a case where repetition is allowed: How many 5 digit numbers can be formed using the digits 1, 2, 3, 4, 5 but with repetition that are divisible by 4? Solution for this question can be given as:
It is clear that number has to be formed using 5 digits only. For a number to be divisible by 4, its last must be divisible by 4. So, units’ digit of number cannot be 1, 3 or 5. If unit digit appears to be 2, then only 12, 32 and 52 are allowed to be last two digits because they are divisible by 4. In case unit digit is 4, then only 24 and 44 are allowed to be last two digits of number. So, total 5 cases (12, 32, 52, 24, and 44) are possible Sets for last two digits of the number.
Now, the first 3 digits of our 5 digit number can be filled in 53 = 125 ways, as repetition of digits is allowed. So, each place can be filled by any of the following digits 1, 2, 3, 4 or 5. So, our desired answer is 125 * 5 = 625 ways.