There are $3$ sections in a question paper and each section contains $5$ questions. A candidate has to answer a total of $5$ questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is
$1500$
$2255$
$3000$
$2250$
If $^n{P_3}{ + ^n}{C_{n - 2}} = 14n$, then $n = $
Ten persons, amongst whom are $A, B$ and $C$ to speak at a function. The number of ways in which it can be done if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is
Let the number of elements in sets $A$ and $B$ be five and two respectively. Then the number of subsets of $A \times B$ each having at least $3$ and at most $6$ element is :
If $^n{C_3} + {\,^n}{C_4} > {\,^{n + 1}}{C_3},$ then
If $^n{C_{r - 1}} = 36,{\;^n}{C_r} = 84$ and $^n{C_{r + 1}} = 126$, then the value of $r$ is