Question

If 4 people, A,B, C and D line up at random, what is the probability that:

a: A and C are next to each other?

b: 1 person is between A and C?

Answer 1

a) here, we need A and C next to each other. so consider A-C to be one person. now, 3 people can be arranged in 3! ways. and A and C can be arranged in 2! ways among themselves. so the total no. of ways for the specified arrangement is 2! 3!.
now all possible ways of arranging those 4 persons is 4!.
so the probability in this case is,
2! 3! / 4!

Answer 2

AC or CA with BD or DB is 4 cases (out of 24)