If $20$ identical books are to be distributed among $4$ persons such that each person receives at least one book,in how many ways can this be done?

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:

$A$ committee of $12$ members is to be formed from $9$ women and $8$ men such that it contains at least $5$ women. Find the number of ways the committee can be formed such that women are in the majority and the number of ways the committee can be formed such that men are in the majority,respectively.

Everybody in a room shakes hands with everybody else. The total number of handshakes is $66$. The total number of persons in the room is

The number of ways in which $21$ identical apples can be distributed among three children such that each child gets at least $2$ apples,is

The total number of different combinations of one or more letters which can be made from the letters of the word $MISSISSIPPI$ is