In a club election the number of contestants is one more than the number of maximum candidates for which a voter can vote. If the total number of ways in which a voter can vote be $62,$ then the number of candidates is :-

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

A person wants to climb a $n-$ step staircase using one step or two steps. Let $C_n$ denotes  the number of ways of climbing the $n-$ step staircase. Then $C_{18} + C_{19}$ equals

In an examination of Mathematics paper, there are $20$ questions of equal marks and the question paper is divided into three sections : $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$. A student is required to attempt total $15$ questions taking at least $4$ questions from each section. If section $A$ has $8$questions, section $\mathrm{B}$ has $6$ questions and section $\mathrm{C}$ has $6$ questions, then the total number of ways a student can select $15$ questions is

Determine the number of $5 -$ card combinations out of a deck of $52$ cards if each selection of $5$ cards has exactly one king.