My textbook has a chapter titled "Permutations with repetitions" in which it discusses certain problems such as scrambling the letters in words which have multiples of some letters. For example:

How many ways are there to rearrange the letters in the word MISSISSIPPI?

What doesn't quite make sense to me is why they use the terminology of permutation:

enter image description here

My intuition tells me these are actually combinations, since it doesn't matter if you have "$S_1 S_2 S_3 S_4$" or "$S_2 S_1 S_3 S_4$" for four adjacent arrangements of the letter "S" in "Mississippi". Indeed, they even use the formulas for combinations in calculating the # of possible arrangements in the above screenshot, so I'm not sure what permutations have to do with it.

  • $\begingroup$ I call these anagrams. $\endgroup$ – Lord Shark the Unknown Jun 29 '17 at 18:32
  • $\begingroup$ Well, that is the technical term, but this is for my notes, and I'd like to avoid confusing myself if possible, so I wanna distinguish between permutations and combinations $\endgroup$ – AleksandrH Jun 29 '17 at 18:33
  • 2
    $\begingroup$ They are called permutations because the order of the letters matters. If, for example, you wanted to count how many ways to choose 5 letters from the letters of MISSISSIPPI, that would be a combination; but if you wanted to count how many ways to place 5 letters from MISSISSIPPI in order, that would be a permutation. $\endgroup$ – user84413 Jun 29 '17 at 18:38
  • $\begingroup$ @user84413 Ahhhhh, that makes perfect sense, thank you!! Right, now that I think about it, MISSISSIPPI $\ne$ MISSIPPSSII $\endgroup$ – AleksandrH Jun 29 '17 at 18:39
  • $\begingroup$ Out of curiosity, what text is this? These are permutations of a multiset. A permutation with repetition is a word of length $n$ formed from a set with $k$ elements. $\endgroup$ – N. F. Taussig Jun 30 '17 at 9:04

The basic difference between permutation and combination is that permutation is "arranging" , combination means how many you can combine without taking into consideration the number of arrangements, or order in some sense. For example no. of two letter word you can make from $\{\ a, b, c \}\ $ is 6 ways.This is permutations. But in how many ways you can choose 2 letters out of three letters "a,b,c". Only 3 ways. This is combination.

Here for the word "Mississippi" you are basically considering permutation.


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