How many different words can be formed by  using all the letters of the word ALLAHABAD? In how many of them vowels occupy the even positions? In how many of them both L do not come together?

Explanation

The given word, 'ALLAHABAD' contains `9 `letters consisting of `4 `A's, `2` L's, `1` H, `1` B and `1` D.


Hence, the number of different words formed by using all the letters of the given word =` (9 !)/((4 !)×(2 !))=7560`.



(ii) Let us take both L together and we treat as `1` letter.



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