Difficult Math Problem #64 - Combinations

[800guy]

In how many ways can the letters of the word 'MISSISIPPI' be arranged?

a) 1260
b) 12000
c) 12600
d) 14800
e) 26800

[gmat_enthus]

C

10!/(4!*3!*2!)

[lalitaroral]

No doubt Its C

[800guy]

OA:

Total # of alphabets = 10
so ways to arrange them = 10!

Then there will be duplicates because 1st S is no different than 2nd S.
we have 4 Is
3 S
and 2 Ps

Hence # of arrangements = 10!/4!*3!*2!

[ashish1354]

i need to understand the logic behind dividing 10! by the repeat factorials of I, S & P can someone please explain??

[cramya]

When u calculate 10! u treat all the letters to be different(Essentially u r saying if I take the first S and put it as starting letter of a word then thats a word and if I take the 2nd S and put it it as starting letter of a word its a different word etc.. But really both are the same words. Since there are 3 S's they could have been arranged in 3! ways You divide by the dupliactes to get to distinct words that could have been formed by these letters)

Similarly for P and I u do the same thing

Hope this helps!