$^n{C_r}{ + ^n}{C_{r - 1}}$ is equal to
$^{n + 1}{C_r}$
$^n{C_{r + 1}}$
$^{n + 1}{C_{r + 1}}$
$^{n - 1}{C_{r - 1}}$
The number of groups that can be made from $5$ different green balls, $4$ different blue balls and $3$ different red balls, if at least $1$ green and $1$ blue ball is to be included
In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation
There are $9$ chairs in a room on which $6$ persons are to be seated, out of which one is guest with one specific chair. In how many ways they can sit
The set $S = \left\{ {1,2,3, \ldots ,12} \right\}$ is to be partitioned into three sets $A,\,B,\, C$ of equal size . Thus $A \cup B \cup C = S$ અને $A \cap B = B \cap C = C \cap A = \emptyset $ . The number of ways to partition $S$ 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