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

The difference between the maximum values of $${ }^6 C_r$$ and $${ }^n C_r$$ is 16, then $$n=$$

If $${ }^{11} \mathrm{C}_4+{ }^{11} \mathrm{C}_5+{ }^{12} \mathrm{C}_6+{ }^{13} \mathrm{C}_7={ }^{14} \mathrm{C}_5$$, then value of $$\mathrm{r}$$ is

If the sum of the mean and the variance of a binomial distribution for 5 trials is 1.8 , then $p=$