All the five-digit numbers in which each successive digit exceeds its predecessor are arranged in increasing order of their magnitude. The $97^{th}$ number in the list does not contain the digit:

The number of ways of choosing $10$ objects out of $31$ objects,of which $10$ are identical and the remaining $21$ are distinct,is

$A$ committee of $12$ members is to be formed from $9$ women and $8$ men such that it contains at least $5$ women. Find the number of ways the committee can be formed such that women are in the majority and the number of ways the committee can be formed such that men are in the majority,respectively.

$A$ question paper consists of two sections having $3$ and $4$ questions respectively. The following note is given on the paper: "It is not necessary to attempt all the questions. One question from each section is compulsory". In how many ways can a candidate select the questions?

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:

In how many ways can $16$ rupees be divided among $4$ persons such that no person receives less than $3$ rupees?