The number of $5$ card combinations out of a deck of $52$ cards such that there is exactly one ace in each combination 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

The total number of ways of selecting six coins out of $20$ one rupee coins,$10$ fifty paise coins,and $7$ twenty-five paise coins is:

$A$ bag contains $23$ balls, of which $7$ are identical. The number of ways of selecting $12$ balls from the bag 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

$A$ student has to answer $10$ out of $13$ questions in an examination,choosing at least $5$ questions from the first $6$ questions. The number of choices available to the student is: