# What is the total number of 8 letter words that can be created using the letters a, a, x, b, c, e, i , o.

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justaguide | Certified Educator

The total number of words that can be created using the letters a, a, x, b, c, e, i , o. has to be determined.

The set of letters given { a, a, x, b, c, e, i , o} has two instances of a.

As the order of letters has to be considered when words are being created, the total number of words that can be created is given by `(P(8, 8))/(2!)` . The number of words would have been P(8, 8) if all the letters were unique. But the letter a has to be used twice, this reduces the total number of words by a factor of `2! = 2` .

The number of different words that can be formed with the letters { a, a, x, b, c, e, i , o} is `(P(8, 8))/(2!)` = `40320/2` = 20160