A probability question I was trying to solve the other reduced to this simple statement:
Find the coefficient of $x^{21}$ in the expansion of:
$$(1+x+x^2+x^3+x^4+x^5)^6$$
Obviously, I can get a computer to do this in seconds, but I would be happier if I could solve the whole problem without computer help. Is there any simple way to answer this question? I've looked at Multinomial expansions, but I can't seem to get them to work.
Thanks