In an election,the number of candidates is $1$ greater than the persons to be elected. If a voter can vote in $254$ ways,then the number of candidates is:

Suppose Anil's mother wants to give $5$ whole fruits to Anil from a basket of $7$ red apples,$5$ white apples,and $8$ oranges. If in the selected $5$ fruits,at least $2$ oranges,at least $1$ red apple,and at least $1$ white apple must be included,then the number of ways Anil's mother can offer $5$ fruits to Anil is $........$

$A$ student has to answer $10$ questions,choosing at least $4$ from each of the parts $A$ and $B$. If there are $6$ questions in part $A$ and $7$ in part $B$,then the number of ways the student can choose $10$ questions is:

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

Mahesh has $6$ friends. In how many ways can he invite one or more friends for dinner?

$A$ committee of $4$ members is to be formed from $4$ couples (husbands and wives). In how many ways can the committee be formed such that no couple is included in the committee?