Multinomial Expansion: Combinations of Letters in MISSISSIPPI Taken 5 at a Time

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Homework Help Overview

The problem involves finding the number of combinations of the letters in the word "MISSISSIPPI" when taken 5 at a time, utilizing multinomial expansion.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to use multinomial coefficients and expresses uncertainty about the next steps in their approach. Some participants suggest expanding the expression while questioning the necessity of keeping terms with exponents less than or equal to 5. Others inquire about potential shortcut methods.

Discussion Status

The discussion is ongoing, with participants exploring different methods of approaching the problem. While some guidance has been offered regarding expansion, there is no explicit consensus on a shortcut or definitive method yet.

Contextual Notes

Participants are navigating the complexities of multinomial expansion and the specific constraints of the problem, including the limitation of selecting letters from a finite set.

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Homework Statement


Find the number of combinations of the letters occurring in the word "MISSISSIPPI" taken 5 at a time.


The Attempt at a Solution



Using multinomials,
The no. of combinations is the coeff. of x5 in the expression
(1+x)(1+x+x2)(1+x+x2+x3+x4)2

I don't know how to proceed after this.
Any help appreciated.
 
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While tedious, I would expand. In the process, you only ever need to keep terms with exponent less than or equal to 5. (Why?)
 
Thanks a lot!...but is there any shortcut method for this?
 
I don't know one. Perhaps.
 

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