$A$ committee of $7$ members is to be formed from $9$ boys and $4$ girls. In how many ways can this be done if the committee consists of at most $3$ girls?

In an examination,a question paper consists of $12$ questions divided into two parts,i.e.,Part $I$ and Part $II$,containing $5$ and $7$ questions,respectively. $A$ student is required to attempt $8$ questions in all,selecting at least $3$ from each part. In how many ways can a student select the questions?

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 all those $3$-digit numbers in which the sum of all the digits in each of them is $10$,is

Number of ways of arranging $8$ identical books into $4$ identical shelves where any number of shelves may remain empty is equal to

In a library,there are $n$ distinct books and each has $p$ copies. What is the number of ways to select one or more books?