How many ways are there to arrange the first five letters of the alphabet?

Question

Jack Russell

Mathematics

6 June, 00:51

How many ways are there to arrange the first five letters of the alphabet?

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Trevor Herring · Answer 1

In probability, problems involving arrangements are called combinations or permutations. The difference between both is the order or repetition. If you want to arrange the letters regardless of the order and that there must be no repetition, that is combination. Otherwise, it is permutation. Therefore, the problem of arrange A, B, C, D, and E is a combination problem.

In combination, the number of ways of arranging 'r' items out of 'n' items is determined using n!/r! (n-r) !. In this case, you want to arrange all 5 letters. So, r=n=5. Therefore, 5!/5! (505) ! = 5!/0!=5!/1. It is simply equal to 5! or 120 ways.