$^n{C_r} + {2^n}{C_{r - 1}}{ + ^n}{C_{r - 2}} = $

The total number of different combinations of one or more letters which can be made from the letters of the word ‘$MISSISSIPPI$’ is

The number of ways in which any four letters can be selected from the word ‘$CORGOO$’ is

${ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}$ if and only if:

In how many ways can one select a cricket team of eleven from $17$ players in which only $5$ players can bowl if each cricket team of $11$ must include exactly $4$ bowlers?

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