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

[zorro]

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.

 

[Tedjn]

While tedious, I would expand. In the process, you only ever need to keep terms with exponent less than or equal to 5. (Why?)

 

[zorro]

Thanks alot!...but is there any shortcut method for this?

 

[Tedjn]

I don't know one. Perhaps.