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How many four-digit numbers are there formed from the digits 1, 2, 3, 4, 5 (with possible repetition) that are evenly divisible by 4?

 Jan 20, 2020
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How many four-digit numbers are there formed from the digits 1, 2, 3, 4, 5 (with possible repetition) that are evenly divisible by 4?

 

If by "possible repetition" you mean permutations such as these:

 

{1, 1, 1, 1}, {1, 1, 1, 2}, {1, 1, 1, 3}, {1, 1, 1, 4}, {1, 1, 1, 5}, {1, 1, 2, 1}, {1, 1, 2, 2}, {1, 1, 2, 3}, {1, 1, 2, 4}, {1, 1, 2, 5}, {1, 1, 3, 1}, {1, 1, 3, 2}, {1, 1, 3, 3}, {1, 1, 3, 4}, {1, 1, 3, 5}, {1, 1, 4, 1}, {1, 1, 4, 2}, {1, 1, 4, 3}, {1, 1, 4, 4}, {1, 1, 4, 5}, {1, 1, 5, 1}, {1, 1, 5, 2}, {1, 1, 5, 3}, {1, 1, 5, 4}, {1, 1, 5, 5}, {1, 2, 1, 1}, {1, 2, 1, 2}, {1, 2, 1, 3}, {1, 2, 1, 4}, {1, 2, 1, 5}, {1, 2, 2, 1}, {1, 2, 2, 2}, {1, 2, 2, 3}, {1, 2, 2, 4}, {1, 2, 2, 5}, {1, 2, 3, 1}, {1, 2, 3, 2}, {1, 2, 3, 3}, {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 4, 1}, {1, 2, 4, 2}, {1, 2, 4, 3}, {1, 2, 4, 4}, {1, 2, 4, 5}, {1, 2, 5, 1}..........etc.

 

Then you will have a total of 625 permutations: In every 25 permutations you have 5 that end in:12, 24, 32, 44 and 52 that are divisible by 4. So 625 / 25 * 5 = 125 such permutations that are divisible by 4.

 Jan 20, 2020

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