Two different numbers are chosen at random from the set {1, 2, 3, ..., 5}. What is the probability that the product of the numbers is even?
The only way to not get an even product is to have two odd numbers. There are (52)=5!2!(5−2)!=10 possible pairs you can choose, and we have three pairs (out of the ten) of odd numbers: (1,3), (1,5), and (3,5). Therefore 1010−310=710.
+1556 
