Question

How many ways are there to choose a 5-letter word from the 26-letter English alphabet with replacement, where words that are anagrams are considered the same

1. ThanhThu
The words need not be English language words  = 142506

### What is Permutation and combination?

In mathematics, there are two alternative methods for dividing up a collection of components into subsets: combination and permutation. The subset’s components can be arranged in any sequence when used together. The components of the subset are arranged in a particular order in a permutation.

### According to the given information:

If the word has 5 different letters  then it is just 26-choose-5 or (26/5).
If the word has 4 different letters  then it is just 26-choose-4 or (26/4)
have 4 options to choose which letter to duplicate twice.
This gives =  4*(26/4)
If the word has 3 different letters  then it is just 26-choose-3 or (26/3).
you duplicate one of the three letters 3 times – 3 options for that, or you choose 2 letters and duplicate each one twice – again 3 options. In total this gives  = 6*(26/3).
If the word has 2 different letters  then it is just 26-choose-2 or (26/2).
The sets of 2 different letters and duplicate either one of the letters 4 times – 2 options; or duplicate one letter 2 times, and the other 3 times – again 2 options. In total this is  = 4*(26/2).
The word has just 1 distinct letter you have =  (26/1).
we get :
N = (26/5)+ 4*(26/4) + 6*(26/3) + 4*(26/2) +  (26/1)
= 142506
The words need not be English language words  = 142506
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