Question

5. There are 10 spots in a parking lot arranged in a single row. Three cars are parked randomly but in such a way that no two cars are adjacent to each other. What is the probability that there are at least two empty spots between any two cars?

Answer 1

Now,

The probability that there are at least two empty spots between any two cars

= 1 - P(no empty spots between any two cars)

$= 1 - \frac{\binom{10-3+1}{3}}{\binom{10}{3}}$

$= 1 - \frac{\binom{8}{3}}{\binom{10}{3}}$

= 1 - 0.466667

=  0.533333