$A$ boy needs to select five courses from $12$ available courses,out of which $5$ courses are language courses. If he can choose at most two language courses,then the number of ways he can choose five courses is

The least value of $n$ such that ${ }^{(n-1)} C_3 + { }^{(n-1)} C_4 > { }^n C_3$ is:

$^nC_{r+1} + ^nC_{r-1} + 2^nC_r = \dots$

The number of ways in which a cricket team of $11$ members can be formed out of $6$ batsmen,$6$ bowlers,$4$ all-rounders and $4$ wicket keepers by selecting at least $4$ batsmen,at least $3$ bowlers,at least $2$ all-rounders and only $1$ wicket keeper is:

If $n$ objects are arranged in a row,then the number of ways of selecting three of these objects such that no two of them are next to each other is:

Compute $\frac{12!}{10! \times 2!}$