If $^n{C_r} = {\,^n}{C_{r - 1}}$ and $^n{P_r}{ = ^n}{P_{r + 1}}$, then the value of $n$ is
$3$
$4$
$2$
$5$
The number of values of $'r'$ satisfying $^{69}C_{3r-1} - ^{69}C_{r^2}=^{69}C_{r^2-1} - ^{69}C_{3r}$ is :-
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 :-
Determine the number of $5 -$ card combinations out of a deck of $52$ cards if each selection of $5$ cards has exactly one king.
If $^n{C_r} = 84,{\;^n}{C_{r - 1}} = 36$ and $^n{C_{r + 1}} = 126$, then $n$ equals
For a scholarship, atmost $n$ candidates out of $2n+1$ can be selected. If the number of different ways of selection of atleast one candidate for scholarship is $63$, then maximum number of candidates that can be selected for the scholarship is -