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?

The English alphabet has $5$ vowels and $21$ consonants. How many words with two different vowels and two different consonants can be formed from the alphabet?

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:

From a group of $10$ men and $8$ women,the number of ways of forming a committee of $8$ members with not more than $5$ men and not less than $5$ women is

Let $S_r = \{(x, y, z) : x + y + z = 11, x \geq r, y \geq r, z \geq r, x, y, z, r \in \mathbb{Z}\}$ and $n(S_r)$ represents the number of elements in $S_r$. Then $n(S_2) + n(S_3) + n(S_4) = $

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