# Prove using Stirling's approximation that for all integers n1 ≥ d1 ≥ 0…

Prove using Stirling's approximation that for all integers n1 ≥ d1 ≥ 0, and all integers n2 ≥ d2 ≥ 0, the following inequality holds: $$\binom{n_1}{d_1}$$*$$\binom{n_2}{d_2}\leq$$ $$(\frac{(n_1+n_2)*e}{(d_1+d_2)})^{d_1+d_2}$$. I tried to use the basics of Stirling's approximation theorem but was of no use as I got stuck and back to the starting point. If you could help me I would be really grateful thanks a ton!