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No of 5 letter english  words that contains atleast one 'a'  ?

i used the approch that

With 26 alphabet for a 5 letter word we can have $26^{5}$ possible words as each 5 position can have 26 possible alphabet.

we need no of word which contains at least one ‘A’.

This is same as

Total number of words – Number of words with no ‘A’

Now,

Number of words with no ‘A’ =$25^{5}$ as, each 5 position can have 25 possible alphabet as we exclude ‘A’.

so ,

Total number of words which contains at least one ‘A’ =$26^{5}-25^{5}$.

i have also same idea as you solve this question but i tried a different approch that does not work , image of my solution is given above plese tell me my mistake , your answer is right
you have over count the number of words.

Case 1:- a_ _ _ _

here ‘aaaaa’ was counted.

case 2:- _a_ _ _

here also ‘aaaaa’ was counted .

same for other cases also happen.

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