The value of $\frac{{ }^{10} \mathrm{C}_{\mathrm{r}}}{{ }^{11} \mathrm{C}_{\mathrm{r}}}$, when both the…
The value of $\frac{{ }^{10} \mathrm{C}_{\mathrm{r}}}{{ }^{11} \mathrm{C}_{\mathrm{r}}}$, when both the numerator and denominator are at their greatest values, is
$\frac{6}{11}$
$\frac{1}{11}$
$\frac{4}{11}$
$\frac{3}{11}$
Solution
Greatest value of ${ }^{-10} \mathrm{C}_{\mathrm{r}}$ is at $\mathrm{r}=5$ Greatest value of ${ }^{11} \mathrm{C}_{\mathrm{r}}$ is at $\mathrm{r}=5$
$\therefore \quad \frac{{ }^{10} \mathrm{C}_{\mathrm{r}}}{{ }^{11} \mathrm{C}_{\mathrm{r}}}=\frac{{ }^{10} \mathrm{C}_5}{{ }^{11} \mathrm{C}_5}=\frac{\frac{10 !}{5 ! 5 !}}{\frac{11 !}{5 ! 6 !}}=\frac{6}{11}$