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In how many different ways can the letters of the word ‘ANNOYING' be arranged?

In how many different ways can the letters of the word ‘ANNOYING' be arranged? Correct Answer 6720

A N N O Y I N G

The above word has total 8 letters, in which 'N' is repeated three times. 

We know that,

Number of ways of arranging ‘n’ distinct letters = n!

Since 'N' is repeated 3 times, no of ways of  = n!/3!

⇒ Total arrangements of = 8!/3! = 6720

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