Two different numbers are chosen at random from 1 to 10. What is the probability that their product is even?

Explanation

1. 01

   The product is odd only when both numbers are odd: ${}^{5}C_2 = 10$ of the ${}^{10}C_2 = 45$ pairs.

2. 02

   So it is even with probability $1 - \frac{10}{45} = \frac{7}{9}$.