If $^n{C_r} = {\,^n}{C_{r – 1}}$ and $^n{P_r}{ = ^n}{P_{r + 1}}$, then the value of $n$ is

In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation

How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ each digit appearing not more than once in each number

$^{n – 1}{C_r} = ({k^2} – 3)\,.{\,^n}{C_{r + 1}}$ if $k \in $

An urn contains $5$ red marbles, $4$ black marbles and $3$ white marbles. Then the number of ways in which $4$ marbles can be drawn so that at the most three of them are red is