Three numbers are chosen at random from numbers 1 to 30. Write the probability that the chosen numbers are consecutive.

Question

Philoid · Accepted Answer

Let E denote the event that the chosen numbers are consecutive.

No of ways in which 3 numbers can be chosen out of 30 = ³⁰C₃

As we have to select 3 consecutive numbers, if we select 1 number other two are already selected.

As 29,30 can’t be selected because if they are selected we won’t be able to get 3 consecutive numbers.

∴ number of ways in which 3 consecutive numbers can be selected = number of ways in which 1 number can be chosen out of numbers from 1 to 28 = ²⁸C₁ ways

∴ P(E) =

Thus, P(E) =