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Three distinct integers are chosen at random and simultaneously from the set {1, 2, 3,..., 50}. What is the probability that the three selected numbers form a set of three consecutive integers?

1. 9 / ((25)(49))
2. 6 / ((25)(49))
3. 3 / ((25)(49))
4. 2 / ((25)(49))

Correct answer: 3 / ((25)(49))

Solution

There are 48 consecutive triples and C(50,3) = 50*49*48/6 = 19600 total selections. The probability is 48/19600 = 3/1225 = 3/((25)(49)), which matches option C.

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