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Question

Three numbers are chosen from 1 to 30. The probability that they are not consecutive, is
  1. 142145
  2. 144145
  3. 143145
  4. 1145

A
142145
B
144145
C
1145
D
143145
Solution
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Probability that the numbers are not consecutive =1probability 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!=1145

Probability that the numbers are not consecutive =11145=144145.

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