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

The solution set of ${ }^5 C_{x-1} > 2 \cdot { }^5 C_x$ is

$A$ student is allowed to choose at most $n$ books from a collection of $2n+1$ books. If the total number of ways in which he can select at least one book is $255$,then the value of $n$ is:

In an election,there are $8$ candidates,out of which $5$ are to be chosen. If a voter may vote for any number of candidates but not greater than the number to be chosen,then in how many ways can a voter vote?

$A$ bag 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 $2$ of them are red is:

In how many ways can a team of $11$ players be formed out of $25$ players,if $6$ out of them are always to be included and $5$ are always to be excluded?