Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals

There are $8$ points in a plane,out of which $4$ are collinear. How many triangles can be formed by joining these points?

In how many ways can $5$ boys and $5$ girls be arranged in a row such that no two girls are together?

How many numbers divisible by $5$ and lying between $3000$ and $4000$ can be formed from the digits $1, 2, 3, 4, 5, 6$ (repetition is not allowed)?

Three parallel straight lines $L_1, L_2$ and $L_3$ lie on the same plane. Consider $5$ points on $L_1, 7$ points on $L_2$ and $9$ points on $L_3$. Then the maximum possible number of triangles formed with vertices at these points is:

Suppose $BC$ is a given line segment in the plane and $T$ is a scalene triangle. The number of points $A$ in the plane such that the triangle with vertices $A, B, C$ (in that order) is similar to triangle $T$ is