An expression of the form (a+b+c+d+ .... ) consisting of sum of many distinct symbols is called a multinomial. Show that `(a+b+c)^n` is the sum of all terms of the form `n!/p!q!e!a^pb^qc^r` where p, q and r range over all possible triples of non negative integers such that p+q+r = n.

Explanation

`(a+b+c)^n` = `sum_(p=0)^n "^nCp a^p (b+c)^(n-p)`
= `sum(n!)/(p!(n-p)!) a^pxx"^(n-p)C_q b^q c^(n-p-q)`
= `sum(n!)/((p!)(n-p1))xx (n-p!)/((q!)(n-p-q!)`
`sum(n!)/((p!q!r!)) a^pb^qc^r (therefore n = p+q+r)`