Presentation on theme: "10-9 Permutations Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation."— Presentation transcript:
10-9 Permutations Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation
Warm Up Find the number of possible outcomes. 1. bagels: plain, egg, wheat, onion meat: turkey, ham, roast beef, tuna 16 Course Permutations
Warm Up Find the number of possible outcomes. 2. eggs: scrambled, over easy, hard boiled meat: sausage patty, sausage link, bacon, ham 12 Course Permutations
Warm Up Find the number of possible outcomes. 3. How many different 4–digit phone extensions are possible? 10,000 Course Permutations
Problem of the Day What is the probability that a 2-digit whole number will contain exactly one 1? Course Permutations 17 90
Learn to find permutations. Course Permutations
Vocabulary factorial permutation Insert Lesson Title Here Course Permutations
Course Permutations and Combinations The factorial of a number is the product of all the whole numbers from the number down to 1. The factorial of 0 is defined to be 1. 5! ! = Read 5! as five factorial. Reading Math
Evaluate each expression. Example 1: Evaluating Expressions Containing Factorials Course Permutations A. 9! = 362,880 8! 6! Write out each factorial and simplify. 8 7 = 56 B. Multiply remaining factors.
Example 1: Evaluating Expressions Containing Factorials Course Permutations and Combinations Subtract within parentheses = ! 7! C. 10! (9 – 2)!
Evaluate each expression. Check It Out: Example 1 Course Permutations A. 10! = 3,628,800 7! 5! Write out each factorial and simplify. 7 6 = 42 B. Multiply remaining factors.
Check It Out: Example 1 Course Permutations Subtract within parentheses = 504 9! 6! C. 9! (8 – 2)!
Course Permutations A permutation is an arrangement of things in a certain order. If no letter can be used more than once, there are 6 permutations of the first 3 letters of the alphabet: ABC, ACB, BAC, BCA, CAB, and CBA. first letter ? second letter ? third letter ? 3 choices2 choices1 choice The product can be written as a factorial = 3! = 6
Course Permutations If no letter can be used more than once, there are 60 permutations (orders) of the first 5 letters of the alphabet, when taken 3 at a time: ABE, ACD, ACE, ADB, ADC, ADE, and so on. first letter ? second letter ? third letter ? 5 choices4 choices3 choices = 60 permutations
Course Permutations ABCABDABEACDACEADEBCDBCEBDECDE ACBADBAEBADCAECAEDBDCBECBEDCED BACBADBAECADCAEDAECBDCBEDBEDCE BCABDABEACDACEADEADBCCEBDEBDEC CABDABEABDACEACEADDCBEBCEBDECD CBADBAEBADCAECAEDADBCECBEDBEDC These 6 permutations are all the same combination. In the list of 60 permutations, each combination is repeated 6 times. The number of combinations is =
Jim has 6 different books. Example 2A: Finding Permutations Course Permutations Find the number of orders in which the 6 books can be arranged on a shelf = There are 720 permutations. This means there are 720 orders in which the 6 books can be arranged on the shelf.
Course Permutations = ! = Use 7! There are 5040 orders in which to arrange 7 soup cans. Check It Out: Example 2A Find the number of orders in which all 7 soup cans can be arranged on a shelf. There are 7 soup cans in the pantry.
Example 2B: Finding Permutations Course Permutations If the shelf has room for only 3 of the books, find the number of ways 3 of the 6 books can be arranged. There are 120 permutations. This means that 3 of the 6 books can be arranged in 120 ways = 6P36P3 The number of books is 6. The books are arranged 3 at a time. = 120
Course Permutations There are 840 permutations. This means that the 7 cans can be arranged in the 4 spaces in 840 ways. = P47P4 The number of cans is 7. The cans are arranged 4 at a time. = 840 There are 7 soup cans in the pantry. Check It Out: Example 2B If the shelf has only enough room for 4 cans, find the number of ways 4 of the 7 cans can be arranged.
Evaluate each expression. 1. 9! There are 8 hot air balloons in a race. In how many possible orders can all 8 hot air balloons finish the race? Lesson Quiz ,880 Insert Lesson Title Here 40,320 Course Permutations 9! 5!