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