USAMO 1975 Problem 1

Show that for any non-negative reals $\mathrm{x}, \mathrm{y},[5 \mathrm{x}]+[5 \mathrm{y}] \geq[3 \mathrm{x}+\mathrm{y}]+[\mathrm{x}+3 \mathrm{y}]$. Hence or otherwise show that (5a)! $(5 b)!/(a!b!(3 a+b)!(a+3 b)!)$ is integral for any positive integers $a, b$.