3-numbers-are-chosen-from-1-to-30-The-probability-that-they-are-not-consecutive-is-

Question Number 18464 by chernoaguero@gmail.com last updated on 22/Jul/17

3 numbers are chosen from 1 to 30 . The

probability that they are not consecutive

is

Answered by Tinkutara last updated on 22/Jul/17

Total number of ways in which a triplet

of 3 numbers can be chosen is^{30} C_{3} .

Now we have 28 pairs of 3 consecutive

integers, i . e . (1, 2, 3), (2, 3, 4), (3, 4, 5),

\dots, (28, 29, 30) .

Probability of these consecutive integers

= \frac{28}{^{30} C_{3}} = \frac{28}{4060} = \frac{1}{145}

∴ Probability that they are not

consecutive integers is = \frac{144}{145}