You and your friend enter a drawing with 4 different prizes. The prizes are awarded randomly. A total of 13 people enter the drawing.
What is the probability that you win first prize and your friend wins second prize?
The probability that you win first prize is 1/13, since there is only one first prize and 13 people entered the drawing.
After you win first prize, there are 12 remaining people in the drawing, so the probability that your friend wins second prize is 1/12.
The probability that you win first prize and your friend wins second prize is the product of the two probabilities:
(1/13) * (1/12) = 1/156