There are $16$ points in a plane, out of which $6$ are collinear. How many lines can be drawn by joining these points?

How many numbers greater than $24000$ can be formed by using the digits $1, 2, 3, 4, 5$ when no digit is repeated?

How many different nine-digit numbers can be formed from the digits of the number $223355888$ by rearranging the digits so that the odd digits occupy even places?

The sum $\sum_{r=1}^{10} (r^2 + 1) \times (r!)$ is equal to

If $\alpha = {^m}{C_2}$,then ${^\alpha}{C_2}$ is equal to

On the sides $AB, BC, CA$ of a $\Delta ABC$,$3, 4, 5$ distinct points (excluding vertices $A, B, C$) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices are: