How can I verify that

[tex]\lim_{N,M,K \to \infty, \frac{M}{N} \to 0, \frac{KM}{N} \to \lambda} \frac{\binom{M}{x}\binom{N-M}{K-x}}{\binom{N}{K}} = \frac{\lambda^x}{x!}e^{-\lambda}[\tex],

withoutusingStirling's formulaor thePoisson approximation to the Binomial?

I have been stuck on this problem for a while, because I don't know how to divide up the terms and factorials without using the help of prior results!

Any help would be appreciated. Thanks in advance.