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"How many words of length 4 can be formed if the letters in the word must be in increasing alphabetical order? Note: {A,A,D,E} is but {A,D,A,E} is not"

The solution is as follows (C denotes choose)

(26 C 1) + (26 C 1)(25 C 1) + (26 C 2) + (26 C 1)(25 C 2) + (26 C 4) = 23751

I am having trouble seeing just what this calculation is doing and why it solves the problem (I've only just recently been introduced to permutations and combinations).

To my understanding, each term in the solution is its own case, but I'm not sure what these cases are.

Any help in explaining this solution would be appreciated.

Thanks.