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

In how many ways can $16$ rupees be divided among $4$ persons such that no person receives less than $3$ rupees?

The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball is:

If ${ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3$,then the minimum value of $n$ is

If $^{2n}C_3 : ^nC_2 = 44:3$,then for which of the following values of $r$,the value of $^nC_r$ will be $15$?

The number of ways of forming a committee of $6$ members out of $5$ Indians,$5$ Americans,and $5$ Australians such that there will be at least one member from each country in the committee is: