Algebra II
Activity:
Permutations
Posted on May 27, 2008
Topic: Permutations, Combinations & Probability
This activity is an introduction to permutations. It includes an optional review on factorials and the Fundamental Counting Principle. Students are then led through the development of the formula for finding n objects taken n at a time and n objects taken r at a time. They are given several problems to solve.
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Activity Key Steps:
In this problem, students use their calculator to investigate factorials and the fundamental counting principle. They evaluate given expressions by using the factorial symbol "!". Students will evaluate the expression 5 • 4• 3 • 2 • 1. Then have students evaluate 5!.
Problem 2 also gives students the opportunity to explore all possible outcomes of spinning a spinner and flipping a coin. They list their answers in the Notes application.
Students study the list they made and form a multiplication expression that can be used to find the answer.
Students move onto Problem 3 where they find the number of ways n objects can be taken r at a time. They explore and define permutations by listing all the ways the letters a, b, and c can be arranged.
They use the nPr command to find the number of permutations.
At the end of this activity, students will be able to use factorial counting principle to calculate the number of outcomes in a sample space. Students will also be able to express the number of permutations and combinations of n elements taken r at a time.