If $^8C_r = ^8C_{r+2}$,then the value of $^rC_2$ is

$A$ set contains $11$ elements. The number of subsets of the set which contain at most $5$ elements is

$A$ linguistic club of a certain Institute consists of $6$ girls and $4$ boys. $A$ team of $4$ members is to be selected from this group,including the selection of a Captain (from among these $4$ members) for the team. If the team has to include at most one boy,the number of ways of selecting the team is:

The product of any $r$ consecutive natural numbers is always divisible by

$A$ lady gives a dinner party for $6$ guests. The number of ways in which they may be selected from among $10$ friends,if two of the friends will not attend the party together,is:

The total number of $3$-digit numbers,whose sum of digits is $10$,is