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In how many different ways can be the letters in the word ARRANGE be arranged.

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ssdixon | Student, Undergraduate | (Level 1) Salutatorian

Posted May 15, 2012 at 5:13 AM via web

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In how many different ways can be the letters in the word ARRANGE be arranged.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 15, 2012 at 5:38 AM (Answer #2)

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There are 7 letters in the word ARRANGE. Of these there are two instances of A. two instances of R and one instance each of N, G and E. The number of ways in which these letters can be rearranged is `(P(7,7))/(2!*2!)`

=> `(7!)/(2!*2!)`

=> `1260`

The letters in the word ARRANGE can be arranged in 1260 different ways.

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