# Probability Using Permutations And Combinations

These lessons help Algebra II students learn to calculate probability using permutations and combinations.

Probability using Permutations (Ordering)
How to use permutations to find the probability of an order under certain conditions?

Example:
Five comedians (Joe, Beth, Seth, Lucial, and Darth) are planning a show. The order of each performance is randomly selected. How many different orders are possible? What is the probability that Joe will go second? What is the probability that Joe will go second and Beth will go last?

Probability with Permutations

Example:
In a classroom there are 13 girls and 15 boys. The class is to elect a President, Vice President, and a Treasurer. What is the probability if students were elected at random that all three positions were filled by boys?

Permutations and Probability

Probability using Combinations
Probability of getting exactly 3 heads in 8 flips of a fair coin.

Probability with Permutations and Combinations

Example:
To win Mr Robb’s Lotto, you must first choose 2 numbers from 1 to 6 and put those numbers in a specific order. You must then choose 3 letters from A to E. What is the probability of winning Mr Robb’s Lotto?

Probability Using Permutations and Combinations

Examples:
Kim and Helen are competing with 3 other students. to get the highest grade in the class. What is the probability that Kim will get the highest grade and Helen the second highest grade?

Jason, Jose, Hans and four other students are left in a drawing for 3 DVDs. What is the probabilty that Jason, Jose, and Hans will each win a DVD?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 