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Example 4-4b Objective Find the number of permutations of a set of objects

Example 4-4b Vocabulary Permutation An arrangement, or listing, of objects in which order is important

Example 4-4b Vocabulary Factorial The expression n! is the product of all counting numbers beginning with n and counting backwards to 1 4! = 4  3  2  1 24

Example 4-4b Math Symbols ! Factorial

Lesson 4 Contents Example 1Evaluate Factorials Example 2Evaluate Factorials Example 3Find a Permutation Example 4Find a Permutation

Example 4-1a Find the value of Write out definition of 4! Multiply using factorial key on calculator Answer: 24 Write problem 1/4

Example 4-1b Find the value of Answer: 120 1/4

Example 4-2a Find the value of the expression Write the definition of 3! Multiply using the calculator Write problem 6  120 Answer: 2/4 Write the definition of 5!

Example 4-2b Find the value of the expression Answer: 144 2/4

Example 4-3a BOWLING A team of bowlers has five members who bowl one at a time. In how many orders can they bowl? Write the definition of the permutation Multiply Answer: Write the permutation 5! 3/4 This is an example of a permutation 5  4  3  2  orders

Example 4-3b TRACK AND FIELD A relay team has four members who run one at a time. In how many orders can they run? Answer: 24 orders 3/4

Example 4-4a RAFFLE A school fair holds a raffle with 1st, 2nd, and 3rd prizes. Seven people enter the raffle. How many ways can the three prizes be awarded? 4/4 This is a modified type of permutation 7 choices for 1st prize 7 Since the person with 1 st place cannot compete for 2 nd place, there only 6 people for 2 nd prize 6 choices for 2nd prize 6 The people that won 1 st and 2 nd prizes cannot compete for 3 rd prize 5 choices for 3rd prize 5

Example 4-4a RAFFLE A school fair holds a raffle with 1st, 2nd, and 3rd prizes. Seven people enter the raffle. How many ways can the three prizes be awarded? 4/4 7 choices for 1st prize 7 6 choices for 2nd prize 6 5 choices for 3rd prize 5 Multiply the numbers 7  6  ways Answer:

Example 4-4b SAILING Nine boats are competing in a sailing race. How many ways can medals for 1st, 2nd, and 3rd place be awarded? Answer: 504 ways * 4/4

End of Lesson 4 Assignment Lesson 9:4Permutations All