The value of $\frac{\binom{10}{r}}{\binom{11}{r}}$, when the numerator and the denominator take thei

Question

The value of $\frac{\binom{10}{r}}{\binom{11}{r}}$, when the numerator and the denominator take their greatest value, is

Professor PC Thomas Classes · Answer

Greatest binomial coefficients are central. $\binom{10}{5} / \binom{11}{5} = \frac{10!}{5!5!} \frac{5!6!}{11!} = \frac{6}{11}$.