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PreCal 12 Unit 6: Permutations and Combinations Lesson 1 NOTES: I. A) Using Counting Principles to Solve Problems: counting methods are used to count members of a specific set and the outcomes of an event. Eg.1: There are 2 styles of kitchen cabinets and 3 finishes that cabinets come in. How many different finished kitchen cabinets are possible? Solution: B) Definition of the Fundamental Counting Principle Suppose an event K can occur in k ways and after it has occurred, event M can occur in m ways. Therefore the number of ways in which K and M can occur is k m ways. Eg. A) How many different 3-digit numbers can be made using seven digits 1,2,3,4,5,6,7 without repetition. B) How many 3-digit numbers are even? C) How many 3-digit numbers are odd? D) How many 3-digit numbers are greater than 300? Solution: C) Factorial Notation: 4! Generally: n! Eg. Show that: A) 5!4! 6 4! Solution: Read as 4 factorial read as n factorial = = 4 3 2 1 24 n (n 1) (n 2) ... 2 1 n! B) (k 1)! k! (k 2)k! Solution: D) Explain the Additive Counting Principle which Implies “OR” statements When 2 events occur independently, you add their results to get the total number of ways an event can occur. This involves drawing up separate cases and adding to get the total number. Eg. 1 How many whole numbers are less than 300? (no repetitions) Solution: Eg. 2 How many different 3-digit numbers that are even and greater than 300 can be formed using 1,2,3,4,5,6,7? Solution: Assignment: Worktext: p. 689-694 #3-16 MC #1-3