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In how many ways can the letters of the word $MISSISSIPPI$ be rearranged ?

I am confused on whether it is $\dfrac{11!}{4!4!2!}$ or $\dfrac{11!}{4!4!2!}-1$

since it is given rearranged and not arranged.

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    $\begingroup$ Those words are usually treated as equivalent for the purposes of such questions (and so the answer would be the former, larger number), but unless you are forced to provide a single numerical value, I see no harm in providing both answers, with justification. $\endgroup$
    – Brian Tung
    Sep 2, 2015 at 18:17
  • $\begingroup$ I would assume that they are expecting the first answer, but I wouldn't expect you to lose points for either. $\endgroup$ Sep 2, 2015 at 18:18
  • $\begingroup$ @BrianTung: These are objective type questions, I need to provide only one answer with options given. $\endgroup$
    – R K
    Sep 2, 2015 at 18:25
  • $\begingroup$ In that case, I would offer the first answer. If they really meant to avoid all respellings, I think they would have explicitly said so. $\endgroup$
    – Brian Tung
    Sep 2, 2015 at 19:54
  • $\begingroup$ If it gives options, it will surely give as a possible answer, only one of the two interpretations ! $\endgroup$ Sep 3, 2015 at 4:13

1 Answer 1

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$$ \frac{11!}{4!4!2!} -1 $$

since $\frac{11!}{4!4!2!}$ is the total number of permutations of the letters from the word MISSISSIPPI.

Since, the word itself is not a rearrangement of itself, that's why a "-1"

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    $\begingroup$ But then there are more to subtract, since many leave the same word MISSISSIPPI in that order. [It is vague, in that does it mean rearrange the physical letters, or just rearrange the positions of the same letters] $\endgroup$
    – coffeemath
    Sep 2, 2015 at 19:35
  • $\begingroup$ @coffee: In such problems, permutations of identical letters don't count, so subtracting 1 (if, indeed, it needs to be subtracted) is correct. $\endgroup$ Sep 3, 2015 at 4:15
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    $\begingroup$ the divison by 4!4!2! is done to remove such repetitions. $\endgroup$
    – user265328
    Sep 3, 2015 at 5:34

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