An urn contains $5$ red marbles,$4$ black marbles and $3$ white marbles. The number of ways in which $4$ marbles can be drawn so that at most three of them are red is

$A$ question paper consists of two sections having $3$ and $4$ questions respectively. The following note is given on the paper: "It is not necessary to attempt all the questions. One question from each section is compulsory". In how many ways can a candidate select the questions?

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 number of ways of selecting a committee of $30$ persons from $20$ boys,$20$ girls,and $20$ teachers such that the participation of the number of boys,girls,and teachers in that committee is equal,is

In how many ways can we select any $4$ letters from the word $CORGOO$?

The value of $r$ for which $^{20}C_r ^{20}C_0 + ^{20}C_{r-1} ^{20}C_1 + ^{20}C_{r-2} ^{20}C_2 + ... + ^{20}C_0 ^{20}C_r$ is maximum is