`X` and `Y` stand in a line with 6 people, What is the probability that there are 3 persons between them

Anita and Binita stand in a line with 7 other people. What is the probability that there are 4 persons between them?

X and Y stand in line at random with 10 other people what is the probability that there are 3 people between X and Y ?

A and B stand in a line with 10 other people. In how many of the permutations there are 3 people between A and B ?

Eight person stand in a line at random. What is the probability that two person X and Y don't stand together.

If six students, including two particular students A and B, stand in a row, then the probability that A and B are separated with one student in between them is

A and B stand in a ring with 10 other persons. If the arrangement of the persons is at random, then the probability that there are exactly 3 persons between A and B is

Three points x, y and z are taken at random on a line segment. What is the probability that z lies between x and y.