This document provides examples of using permutations and combinations to calculate probabilities of events occurring. It discusses: - Calculating the probability of selecting two white and two red balls from an urn containing six white and five red balls by finding the number of ways to choose two white and two red balls, and dividing by the total number of possible outcomes. - Calculating probabilities for other events involving selecting balls from urns with different ball combinations. - Calculating probabilities for events involving selecting students for a team from groups with different numbers of boys and girls. - Calculating the probability of choosing a specific letter from a word by counting the number of ways to choose that letter and dividing by the total letters.