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

$A$ 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?

If ${ }^{n-3} C_r + B \cdot { }^{n-3} C_{r-1} + B^{\prime} \cdot { }^{n-3} C_{r-2} + { }^{n-3} C_{r-3} = { }^n C_r$ holds for all $n \geq r \geq 3$,then $(B, B^{\prime}) = $.

What is the number of ways in which an examiner can assign $10$ marks to $4$ questions,giving not less than $2$ marks to any question?

If $\binom{n-1}{r} = (k^2 - 3) \binom{n}{r+1}$,then $k \in \dots$

Out of $10$ white,$9$ black and $7$ red balls,the number of ways in which selection of one or more balls can be made,is