Posted by **Esmeralda** on Friday, December 9, 2011 at 10:34pm.

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?

- Math -
**Reiny**, Friday, December 9, 2011 at 11:32pm
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

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