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?

Determine the number of $5$ card combinations out of a deck of $52$ cards if there is exactly one ace in each combination.

If a question paper consists of $11$ questions divided into two sections,$I$ and $II$. Section $I$ consists of $6$ questions and section $II$ consists of $5$ questions,then the number of different ways a student can select $6$ questions,taking at least $2$ questions from each section,is

The number of integers between $10$ and $10,000$ such that in every integer every digit is greater than its immediate preceding digit,is

If $x, y$ and $r$ are positive integers,then $^x{C_r} + ^x{C_{r-1}} ^y{C_1} + ^x{C_{r-2}} ^y{C_2} + \dots + ^y{C_r} = $

The number of ways $16$ identical cubes,of which $11$ are blue and the rest are red,can be placed in a row so that between any two red cubes there should be at least $2$ blue cubes,is