If $\binom {28}{2r} : \binom {24} {2r-4} = 225:11$, find $r$.

Question

I want to know what should be a good and efficient approach to solve the given question (and similar questions):

If $\binom {28}{2r} : \binom {24} {2r-4} = 225:11$, find r.

Answer 1

Hint

Use $$\binom {n}{k}=\binom {n}{n-k}$$ to get

$$\frac {\binom {28}{2r}}{\binom {24}{2r-4}}=\frac {\binom {28}{28-2r}}{\binom {24}{28-2r}}=\frac {225}{11}$$

Put $28-2r=k$

Hence $$\frac {\binom {28}{k}}{\binom {24}{k}}=\frac {225}{11}$$