In a conference of $8$ persons,if each person shakes hands with every other person exactly once,then the total number of handshakes is:

$A$ country has $10$ smart cities. The government decides to connect all these cities by road. How many roads does the government need to construct so that every city is connected to every other city?

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:

Assuming the balls to be identical except for the difference in colours,the number of ways in which one or more balls can be selected from $10$ white,$9$ green,and $7$ black balls is:

If $^{43}C_{r-6} = ^{43}C_{3r+1}$,then the value of $r$ is

There are $3$ girls in a class of $10$ students. The number of different ways in which they can be seated in a row such that no two of the three girls are together is