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

In how many ways can a committee,consisting of $5$ men and $6$ women,be formed from $8$ men and $10$ women?

In how many ways can $mn$ letters be posted in $n$ letter-boxes?

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by $66$,then the number of men who participated in the tournament lies in the interval

Total number of $3$ letter words that can be formed from the letters of the word $'SAHARANPUR'$ is equal to

$A$ question paper has $2$ parts,part $A$ and part $B$,each containing $10$ questions. If a student has to choose $8$ questions from part $A$ and $5$ questions from part $B$,in how many ways can the student choose the questions?