If ${ }^{2n } C _3:{ }^{n } C _3=10: 1$, then the ratio $\left(n^2+3 n\right):\left(n^2-3 n+4\right)$ is

A car will hold $2$ in the front seat and $1$ in the rear seat. If among $6$ persons $2$ can drive, then the number of ways in which the car can be filled is

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty

Out of $10$ white, $9$ black and $7$ red balls, the number of ways in which selection of one or more balls can be made, is

In the $13$ cricket players $4$ are bowlers, then how many ways can form a cricket team of $11$ players in which at least $2$ bowlers included

In how many ways a team of $10$ players out of $22$ players can be made if $6$ particular players are always to be included and $4$ particular players are always excluded