Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $f=x+y+xz+yw$ where $x,y,z,w$ are variables. Let $S=\{\mbox{ monomials of }f^{20}\}$. How can I calculate the product of elements of $S$ and cardinality of $S$?

share|cite|improve this question
up vote 1 down vote accepted

First note that all the monomials in the expansion


are distinct. Thus there are as many of them as partitions of $20$ into four parts with zeros allowed. Of these there are $\binom{20+4-1}{4-1}=\binom{23}3=1771$.

As for the product, by symmetry each of the terms will occur the same number of times as a factor, so we only have to count how many times one term, say $x$, occurs. There are


different monomials with $n_x$ factors of $x$, so the total number of factors of each term in the product is


Thus the product is


share|cite|improve this answer
Thanks for the help. – user12290 Aug 21 '11 at 9:16

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.