Permutations and Combinations

1. Permutations and Combinations PRE-ALGEBRA LESSON 12-6 Bianca’s family needs to choose exterior paint for their new house. The wall colors are white, green, and beige. The trim colors are white, green, blue, and cocoa. How many combinations of wall color and trim are possible? 12 12-6

2. Permutations and Combinations PRE-ALGEBRA LESSON 12-6 (For help, go to Lesson 12-4.) Use the Counting Principle to find the number of outcomes. 1. Roll 2 number cubes. 2. Choose three different letters. 3. Select a month and a day of the week. 4. Toss a coin 4 times. Check Skills You’ll Need 12-6

3. Permutations and Combinations PRE-ALGEBRA LESSON 12-6 Solutions 1.first numbersecond number 6 outcomes 6 outcomes 6  6 = 36 2.first lettersecond letterthird letter (different from 1st)(different from 1st & 2nd) 26 choices 25 choices 24 choices 26  25  24 = 15,600 12-6

4. Permutations and Combinations PRE-ALGEBRA LESSON 12-6 Solutions (continued) 3.monthday 12 choices 7 choices 12  7 = 84 4.first tosssecond tossthird tossfourth toss 2 outcomes 2 outcomes 2 outcomes 2 outcomes 2  2  2  2 = 16 12-6

5. 1st letter 5 choices 5 2nd letter 4 choices 4 3rd letter 3 choices 3 4th letter 2 choices 2 5th letter 1 choice 1 = 120 • • • • Permutations and Combinations PRE-ALGEBRA LESSON 12-6 Find the number of permutations possible for the letters H, O, M, E, and S. There are 120 permutations of the letters H, O, M, E, and S. Quick Check 12-6

6. 7 studentsChoose 3. 7P3 Permutations and Combinations PRE-ALGEBRA LESSON 12-6 In how many ways can you line up 3 students chosen from 7 students for a photograph? = 7 • 6 • 5 = 210 Simplify You can line up 3 students from 7 in 210 ways. Quick Check 12-6

7. State Area (mi2) Alabama Colorado Maine Oregon Texas 50,750 103,729 30,865 96,003 261,914 Permutations and Combinations PRE-ALGEBRA LESSON 12-6 In how many ways can you choose two states from the table when you write reports about the areas of states? Make an organized list of all the combinations. 12-6

8. Permutations and Combinations PRE-ALGEBRA LESSON 12-6 (continued) AL, COAL, MEAL, ORAL, TXUse abbreviations of each CO, MECO, ORCO, TXstate’s name. First, list all ME, ORME, TXpairs containing Alabama. OR, TXContinue until every pair of states is listed. There are ten ways to choose two states from a list of five. Quick Check 12-6

9. 9 toppingsChoose 5. 9C5 9P5 5P5 = 9 • 81 • 7 • 62 • 51 51 • 41 • 31 • 21 • 1 = = 126 Simplify. Permutations and Combinations PRE-ALGEBRA LESSON 12-6 How many different pizzas can you make if you can choose exactly 5 toppings from 9 that are available? You can make 126 different pizzas. Quick Check 12-6

10. Permutations and Combinations PRE-ALGEBRA LESSON 12-6 Tell which type of arrangement—permutations or combinations—each problem involves. Explain. a.  How many different groups of three vegetables could you choose from six different vegetables? b.  In how many different orders can you play 4 DVDs? Combinations; the order of the vegetables selected does not matter. Permutations; the order in which you play the DVDs matters. Quick Check 12-6

11. Permutations and Combinations PRE-ALGEBRA LESSON 12-6 Find the number of permutations or combinations. 1. Find the number of permutations of the last four digits in the phone number 555–1234. 2. In how many ways can you arrange six out of eight books on a shelf? 3. In how many ways can you choose three different items from a menu containing seven items? Does each problem involve permutations or combinations? 4. How many different groups of four ice cream toppings can you choose from sixteen toppings? 5. In how many different ways can five students line up? 24 20,610 35 combinations permutations 12-6