Question

Three numbers are chosen from $1$ to $30$ . Find the probability that they are not consecutive.

• A. $\frac{16}{81}$
• B. $\frac{144}{145}$
• C. $\frac{80}{145}$
• D. $\frac{65}{81}$

Answer 1

Answer: (B)

The total number of ways in which $3$ numbers can be chosen out of $30$ numbers ${=}^{30}{C}_3=4060$ . The number of ways of choosing $3$ consecutive numbers is $28$ .
Therefore, the number of ways in which the three numbers chosen are not consecutive is $4060-28=4032$ .
Hence, the required probability $=\frac{4032}{4060}=\frac{144}{145}$