Three numbers are chosen from 1 to 20. The probability that they are not consecutive is
187190
Number of ways to choose three numbers from 1 to 20 = 20C3=1140
Now, the set of three consecutive numbers from 1 to 20 are (1, 2, 3), (2, 3, 4), (3, 4, 5), ..........., (18, 19, 20).
So, the number of ways to choose three numbers from 1 to 20 such that they are consecutive is 18.
P(three numbers choosen are consecutive)
Number of ways to choose three
=consecutive number from 1 to 20Number of ways to choose three
numbers from 1 to 20
=1820C3=181140=3190
P(three numbers choosen are not consecutive) = 1 - P(three numbers choosen are consecutive)
=1−3190=187190
Hence, the correct answer is option (b).