Counting and Probability

Question

If there are 36 runners in a race and prizes will be awarded to first, second, and third places only, what is the probability of correctly predicting the winners in order?

??(Express as a fraction.)

If there are 36 runners in a race and prizes will be awarded to first, second, and third places only, what is the probability of correctly predicting the winners in order?   (Express as a fraction.)

Answer 1

Assuming that the probability of a runner finishing in a particular position is the same for all runners...

 

The probability of picking the first place finisher is 1/36.  Then there are only 35 runners to choose from for second place, so the probability of picking that correctly is 1/35.  And then there are only 34 runners for third place, so the probability is 1/34.  So the probability of picking all of the first three positions is 1/36 * 1/35 * 1/34 = 1/42840