If the number of five digit numbers with distinct digits and $2$ at the $10^{\text {th }}$ place is $336 \mathrm{k}$, then $\mathrm{k}$ is equal to
$8$
$6$
$4$
$2$
If $^{n + 1}{C_3} = 2{\,^n}{C_2},$ then $n =$
Let $A = \left\{ {{a_1},\,{a_2},\,{a_3}.....} \right\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of it is formed independently. The number of ways in which subsets can be formed such that $(P-Q)$ contains exactly $2$ elements, is
If $\alpha { = ^m}{C_2}$, then $^\alpha {C_2}$is equal to
If $\frac{{{}^{n + 2}{C_6}}}{{{}^{n - 2}{P_2}}} = 11$, then $n$ satisfies the equation
In how many ways $5$ speakers $S_1,S_2,S_3,S_4$ and $S_5$ can give speeches one after the other if $S_3$ wants to speak after $S_1$ & $S_2$