Three different numbers are chosen at random from the set {1,2,3,4,5}. The numbers are arranged in increasing order. What is the probability that the resulting sequence is an arithmetic sequence?

Answer 1

Since the order has to be increasing , the only possibilities are
1 2 3
2 3 4 , common difference of 1 for these three choices
3 4 5
1 3 5 , common difference of 2
(there are not enough numbers to have a common difference of 3)

The total number of triplets we can form are
5x4x3 = 60

Prob that our triplet forms an arithmetic sequence = 4/60 = 1/15