Three numbers are chosen at random from numbers 1 to 20 . The probability that they are consecutive is

Step-by-step solution

The sample space consists of all 3-element subsets of S = 1, 2, , 20 , yielding 20 3 = 20 19 18 3 2 1 = 1140 equally likely outcomes. Consecutive triplets correspond to sets of the form x, x+1, x+2 where 1 x 18 . There are 18 such sets, as the smallest starting value is 1 and the largest is 18. The probability is thus 18 1140 = 3 190 , matching option C .