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Question

Three numbers are chosen from 1 to 30. The probability that they are not consecutive, is

A
142145
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B
144145
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C
143145
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D
1145
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Solution

The correct option is B 144145Probability that the numbers are not consecutive =1−probability of the numbers being consecutive.Given numbers from 1to30∴ sample space is 30!Making groups of 3 consecutive numbers from (1,2,3) to (28,29,30) we will get 28 pairs.Considering 3 numbers as single digit, the numbers will be 28 and those three numbers can be arranged in 3 different ways.Three numbers consecutively =28!×3!∴Probability=28!×3!30!=1145Probability that the numbers are not consecutive =1−1145=144145.

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