How many combinations are there to arrange the letters in MISSISSIPPI requiring that the 2 S's must be separated?
I found there are 34650 combinations to arrange without restriction.
How to approach this question?
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'won't be stick' - what does it mean? – Alex Mar 03 '14 at 14:19
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Spelling it right is a good start. Or is there only one P in your homework? – Daniel R Mar 03 '14 at 14:19
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fixed, sorry for the mistakes. – opeer Mar 03 '14 at 14:21
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are you familiar with inclusion-exclusion theorem? – Alex Mar 03 '14 at 14:23
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@Alex yes I do. – opeer Mar 03 '14 at 14:25
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2there are 4 S's in MISSISSIPI though? – Guy Mar 03 '14 at 14:36
2 Answers
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We know that the string will take the form of
$$*S█S█S█S*$$
where $█$ MUST have at least one character and $*$ can be of any length (even 0). I would suggest the following steps:
- Find the number of ways you can put the $S$s (they can be in positions $(1,3,5,7)$, $(2,5,8,11)$, $(1,4,6,9)$, etc.)
- Find the number of different strings you can make with $MIIIPPI$ (that's $MISSISSIPPI$ without the $S$s)
- Multiply the two.
I leave the math for you to do.
2012ssohn
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Find all possible ways we can arrange MIIIPPI: 7!/(4!*2!). Then "insert" four S into the 8 space between each possible arrangement of MIIIPPI, e.g. [1]M[2]I[3]I[4]I[5]P[6]P[7]I[8]; This is really ${8}\choose{4}$. Multiplying the two!
Daniel Li
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