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From a set of 11 consecutive natural numbers, three numbers are chosen at random without replacement. What is the probability that the chosen numbers form an arithmetic progression with a positive common difference?
- 15/101
- 5/101
- 5/33
- 10/99
Correct answer: 5/33
Solution
With 11 consecutive naturals, the number of valid APs is found by summing over d from 1 to 5 the number of valid starting terms. Dividing by C(11,3) = 165 gives the probability.
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