The value of $^{15}C_{3} + ^{15}C_{13}$ is

In how many ways can a committee of $6$ members be formed out of $10$ members,such that it always includes a specified member?

If $\binom{n+1}{3} = 2 \times \binom{n}{2}$,then $n = \dots$

Given $5$ different green toys,$4$ different blue toys,and $3$ different red toys,how many combinations of toys can be chosen taking at least one green and one blue toy?

$^nC_r + ^nC_{r-1}$ is equal to

Five students are selected from $n$ students such that the ratio of the number of ways in which $2$ particular students are selected to the number of ways $2$ particular students are not selected is $2:3$. Then the value of $n$ is