Probability 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!=1145
Probability that the numbers are not consecutive =1−1145=144145.