The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball, is

A set contains $(2n + 1)$ elements. The number of sub-sets of the set which contains at  most $n$ elements 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

If $\sum\limits_{i = 0}^4 {^{4 + 1}} {C_i} + \sum\limits_{j = 6}^9 {^{3 + j}} {C_j} = {\,^x}{C_y}$ ($x$ is prime number), then which one of the following is incorrect 

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?