In how many ways can a team of $3$ boys and $3$ girls be selected from $5$ boys and $4$ girls?

If $^{n^2 - n}C_2 = ^{n^2 - n}C_{10}$,then $n = $

The total number of ways of forming a committee of $5$ members out of $7$ Indians,$6$ Americans,$5$ Russians,and $4$ Australians such that every committee contains at least one member from each country is:

The number of ways in which a committee of $6$ members can be formed from $8$ gentlemen and $4$ ladies so that the committee contains at least $3$ ladies is

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:

In a football championship,there were played $153$ matches. Every team played one match with each other. The number of teams participating in the championship is