Putnam 1984 A5

Problem A-5 Let $R$ be the region consisting of all triples ( $x, y, z$ ) of nonnegative real numbers satisfying $x+y+z \leqslant 1$. Let $w=1-x-y-z$. Express the value of the triple integral $$\iiint_{R} x^{1} y^{9} z^{8} w^{4} d x d y d z$$ in the form $a!b!c!d!/ n!$, where $a, b, c, d$, and $n$ are positive integers.