The greatest integer which divides $(p+1)(p+2)(p+3) \ldots (p+q)$ for all $p \in N$ and fixed $q \in N$ is

The number of ways of distributing $8$ identical rings to $3$ different girls so that every girl gets at least $1$ ring is

If ${ }^{11} C_4+{ }^{11} C_5+{ }^{12} C_6+{ }^{13} C_7={ }^{14} C_{r}$,then the value of $r$ is

From a class of $25$ students,$10$ are to be chosen for an excursion party. There are $3$ students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

The total number of ways of forming a committee of $5$ members out of $7$ Indians,$6$ Americans,$5$ Russians,and $4$ Australians such that every committee contains at least one member from each country is:

Out of $10$ white,$9$ black and $7$ red balls,the number of ways in which selection of one or more balls can be made,is