# How many words can be formed with the letters of word 'APTITUDE', with repetition of letters is allowed?

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How many words can be formed with the letters of word 'APTITUDE', with repetition of letters is allowed?
1. 8!
2. $8^8\over2!$
3. 78
4. $7^8\over2!$

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Correct Answer - Option 3 : 78

Calculation:

There are 8 places and 7 letters 'A', 'P', 'T', 'I', 'U', 'D', 'E'

Each of the 8 places can have any of the 7 letters

∴ Numbers of words that can be formed = 78