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in how many different ways can the letters of the word MISSISSIPPI be arranged ??

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reemamoun | Student, Grade 10 | eNotes Newbie

Posted May 23, 2010 at 4:14 AM via web

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in how many different ways can the letters of the word MISSISSIPPI be arranged ??

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted May 23, 2010 at 4:17 AM (Answer #1)

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Since there are 11 letters of the word MISSISSIPPI, then the number of words could be arranged is 11! ways.

However, there are 4 I's, 4 are S's and 2 are P's.

Then, we need to eliminate the number of the repeated words.

Then the number of words is 11!/2!4!4! = 34,650

 

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neela | High School Teacher | Valedictorian

Posted May 23, 2010 at 9:17 AM (Answer #2)

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If There are n different letters, they could be permuted in nPn = n! different arrangements.

If  out of n things p of  them of them are alike, another q of them are them are alike and still another r of them are alike  then the number of arragements is equal to n!/(p1*q!*r!).

In mississipi , the alphabets are 11. there are 4 letters s alike. Two letters are i's alike. So the number of permutations of 11 letters of which 4 are  s alike and another 2 are i alike is = 11!/(4!*2!) = 831600

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