Introductory Statistics Lesson 3.4 A Objective: SSBAT determine the number of permutations. Standards: M11.E.3.2.1

Permutation  An arrangement of data where order is IMPORTANT  ABC is not the same as CBA  Can use the Fundamental Counting Principle to find  Can also find the number of different permutations of n distinct objects using n!

n!  Read as n factorial  Defined as: n! = n(n – 1)(n – 2) (n – 3) ···3·2·1 Examples: 5! 9! = 5 · 4 · 3 · 2 · 1 = 120 = 9 · 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1 = 362,880

There is a factorial key on the calculator  Go to MATH  Scroll over to PRB  Then choose #4 which is ! Practice: 8! 12! 10! – 4! = 40,320 = 479,001,600 = 3,628,776

Example: Find the number of ways 6 people can finish a race. Method 1: Fundamental Counting Principle 6 · 5 · 4 · 3 · 2 · 1 = 720 Method 2: Permutation 6! = 720

Answer: 840 Answer: 99,638,080,820,000

2.The board of directors for a company has 12 members. One member is the president, another is the vice-president, another is the secretary, and another is the treasurer. How many ways can these positions be assigned?

3.A museum is going to hang 9 paintings on a wall from left to right. How many different ways can the museum hang these 9 paintings on the wall?

Complete Worksheet 3.4 A