2 2 Students may conjecture that it is equal to r. 20 5 P2 and ask what the number in the denominator might represent. The division template can be accessed by / + p. Students should write a fraction using permutation notation (i.e., n Pr ) to represent the number of combinations. In this instance, the number of combinations is 20 ÷ 2. They should find that there are half as many combinations as permutations. Ask students how the number of combinations compares to the number of permutations. Once all the desired permutations have been hidden, pressing the d key closes out of Hide/Show. They should select Hide/Show from the Tools menu and click on each arrangement to be hidden. Explain that when finding combinations, ab is the same as ba the order does not matter-both name the same group. Problem 2 – Combinations Students should read page 2.1 and advance to page 2.2, where they will reduce the displayed permutations to combinations. Later in this activity, students will answer the same question using combinations.
Have students enter their amount by clicking twice on diagonals=1 and entering their amount. (Students should find a total of nine diagonals). If needed, remind them that a diagonal is a segment joining two nonadjacent vertices. Problem 1 – An introduction Have students move to page 1.2 and find the number of diagonals in a hexagon by using the Segment tool from the Points & Lines menu.
FACTORIAL ON TI NSPIRE PLUS
Permutations & Combinations (TI-Nspire technology) - 12602 What’s Your Combination (TI-84 Plus family) - 10126 Perms and Combs? (TI-Nspire technology) - 12645
FACTORIAL ON TI NSPIRE DOWNLOAD
Associated Materials Combinations_Student.doc Combinations.tns Combinations_Soln.tns Suggested Related Activities To download any activity listed, go to education.ti.com/exchange and enter the number in the keyword search box. To download the student and solution TI-Nspire documents (.tns files) and student worksheet, go to education.ti.com/exchange and enter “8433” in the keyword search box.
The use of the Navigator System is not necessary for completion of this activity. Notes for using the TI-Nspire™ Navigator™ System are included throughout the activity. For this reason, it is important that you do not rush through the activity or assume that any part of the activity is “too easy.” A solid foundation on these basic concepts will help them later when the problems become more complex. Many students struggle with permutations and combinations. This activity assumes that students have previous knowledge of finding permutations. It can also be used in an introductory Statistics course or an advanced Algebra 1 course. Teacher Preparation and Notes This activity is designed to be used in an Algebra 2 classroom. Evaluate expressions involving factorials to compute the number of outcomes in a sample space.
Topic: Permutations, Combinations & Probability Use factorial notation to express the number of permutations and combinations of n elements taken r at a time. Students then solve several problems involving combinations, including problems that involve geometry. From here they see how the number of combinations is related to the number of permutations. They derive the formula for the number of combinations of n objects taken r at a time by starting with a list of permutations and eliminating those that name the same group, just in a different order. Activity Overview This activity introduces students to combinations.
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