Three numbers are chosen at random from 1 to 15. Probability that no two numbers are consecutive is

Question

Very urgent

Answer 1

there are 15C2 pairs from 15 numbers ... (15 * 14) / (2 * 1) = 105

there are 14 consecutive pairs from 15 consecutive numbers

probability that a pair is NOT consecutive ... (105 - 14) / 105 = 91 / 105

three numbers is three distinct pairs

probability of no consecutive pairs in three numbers ... (91 / 105)^3