if three distinct numbers are selected from the set of first 20 natural numbers, then the probability that they are in GPis equal to?

Option 3 is correct answer.We will use smart way to calculate first according to probability any event probability is= no of favourable outcome/total outcomeSol: Total outcome is 20C3 or 20!/17!×3! =20×19×18/3!=20×19×3=60×19=1140 .Now no of fav outcome is 16.You can find it by simple observation and gp simple form.Now probablity is 16/1140=4/285;Hence 3rd option is required answer