The number of ways in which $17$ apples can be distributed among $4$ guests such that each guest gets at least $3$ apples is

The number of ways in which a team of $11$ players can be formed out of $25$ players,if $6$ out of them are always to be included and $5$ of them are always to be excluded,is

$A$ committee of $4$ persons is to be formed from $2$ ladies,$2$ old men,and $4$ young men such that it includes at least $1$ lady,at least $1$ old man,and at most $2$ young men. The total number of ways in which this committee can be formed is:

$A$ man has $10$ friends. In how many ways can he invite one or more of them to a party?

If $n$ objects are arranged in a row,then the number of ways of selecting three of these objects such that no two of them are next to each other is:

The number of ways in which an examiner can assign $30$ marks to $8$ questions,awarding not less than $2$ marks to any question is