(related to Proposition: Multinomial Coefficient)
The number of words, which can be created out of the letters of the word MISSISSIPPI is
\[\frac{11 ! }{4 ! 4 ! 2 ! 1 !}=34,650\]
One of such words (without any meaning) could be SIPISMSIPIS.
The binomial coefficient is a special case of the multinomial coefficient, since
\[\binom nk=\binom n{k,n-k}=\frac{n ! }{k !\cdot (n-k) ! }.\]
The coefficient of the term \(x^2y^3z^5\) by calculating \((x +y +z)^{10}\) is
\[\binom {10}{2,3,5}=\frac{10 ! }{2 ! 3 ! 5 !}=2520.\]
