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
$1500$
$2255$
$3000$
$2250$
${ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}$ if and only if:
The number of ways in which we can select three numbers from $1$ to $30$ so as to exclude every selection of all even numbers is
If $^n{P_r} = 840,{\,^n}{C_r} = 35,$ then $n$ is equal to
From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :
A person is permitted to select at least one and at most $n$ coins from a collection of $(2n + 1)$ distinct coins. If the total number of ways in which he can select coins is $255$, then $n$ equals