# Weird limits

Calculus Level 5

$\large \lim _{ n\rightarrow \infty }{ \binom{n}{7} { p }^{ 7 }{ q }^{ n-7 } }=\frac {{e}^{A}{B}^{C}}{D!}\$

Given the above, where $$p+q=1$$ and $$np=5$$, find $$A+B+C+D$$.

Bonus: Generalize for $$r$$ and $$m$$ in place of 7 and 5 respectively.

Notation: $$\displaystyle \binom{n}{r}=\frac{n!}{(n-r)!r!}$$ denotes the binomial coefficient.

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