In how many ways can a committee of $5$ members be formed from $4$ gentlemen and $6$ ladies such that the number of gentlemen is greater than the number of ladies?

$A$ company has $10$ employees. The company has decided to form a team including at least three employees and also excluding at least three employees. Then the number of ways of forming the team is

$A$ student is asked to answer $10$ out of $13$ questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is

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

If $^{10}C_r = ^{10}C_{r+2}$,then $^5C_r$ equals

$A$ group consists of $8$ boys and $5$ girls. The number of committees of $5$ persons that can be formed,if the committee consists of at least $2$ girls and at most $2$ boys,is: