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Today’s Agenda

Pre- Calculus 2. Today’s Agenda. Due TODAY: HW #48 Handout – Probability of Ind. Events Due TOMORROW: HW # 49 Handout – Intro to Permutations. 1. Do Now. Notes: Permutations. 3. Classwork. 4. Summary. SWBAT…. Define a permutation Calculate the number of permutations

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Today’s Agenda

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  1. Pre-Calculus 2 Today’s Agenda Due TODAY:HW #48 • Handout – Probability of Ind. Events • Due TOMORROW: HW #49 • Handout – Intro to Permutations • 1. Do Now • Notes: • Permutations 3. Classwork 4. Summary SWBAT… • Define a permutation • Calculate the number of permutations • Calculate the probability of a permutation

  2. permutations Fundamental countingprinciple How many different license plates are possible if a license plate must be: ##LL## 10 ∙ 10 ∙ 26∙ 26 ∙ 10∙ 10 = 6,760,000

  3. permutations Arrangementswithoutreplacement How many different license plates are possible if a license plate must be: ##LL## AND no letters or numbers are repeated? 10 ∙ 9 ∙ 26∙ 25 ∙ 8∙ 7 = 3,276,000

  4. ARRANGEMENTS WITHOUT REplacement permutations What is the probability that a license plate will have no repeated letters or numbers?

  5. ARRANGEMENTS WITHOUT REplacement permutations permutations Your sister just got married. She had 7 bridesmaids whose names were listed in the wedding program in random order. Since there were 7 bridesmaids, there were 7 possible choices for the first slot. • How many ways could their names have been listed?

  6. ARRANGEMENTS WITHOUT REplacement permutations permutations How many ways could their names have been listed? Which means there are only 6 bridesmaids that can be named in the second slot. and so on…

  7. ARRANGEMENTS WITHOUT REplacement permutations permutations • How many ways could their names have been listed? There are 5,040 ways to list the names of seven bridesmaids

  8. ARRANGEMENTS WITHOUT REplacement permutations permutations What is the probability their names were in alphabetical order? There is only 1 way to alphabetize their names, so….

  9. ARRANGEMENTS WITHOUT REplacement permutations permutations After the wedding, they took pictures. Four bridesmaids were seated and 3 stood behind them. This time, there are only 4 slots but any of the 7 bridesmaids could be in the first slot. • How many possible seating arrangements were there?

  10. ARRANGEMENTS WITHOUT REplacement permutations permutations Which means there are only 6 bridesmaids remaining to choose from. and so on… • How many possible seating arrangements were there?

  11. ARRANGEMENTS WITHOUT REplacement permutations permutations … until all the there were no more seats. • How many possible seating arrangements were there? There are 840 ways to seat four bridesmaids in the front

  12. permutations Apermutationis an arrangement of some or all of the objects from a set, without replacement. The number of permutations of nobjects chosen r at a time is: What the heck does that mean?

  13. BridesmaidsExample In our picture-taking example, there were 7 bridesmaids and 4 seated spaces. n = number of options r = number of spaces available

  14. BridesmaidsExample Simplify! An expression #! is called a factorial. It is a symbol that means the product of the integers from that number all the way down to one.

  15. BridesmaidsExample An expression #! is called a factorial. It is a symbol that means the product of the integers from that number all the way down to one.

  16. Didweachieveourobjectives? • Today’s Objectives: • SWBAT… • Define matrices • Name the parts of matrices • Identify commensurate matrices • Find the sum of two matrices • Find the difference of two matrices Due TOMORROW HW #37: • Handout – Section 7.2 #1 – 21

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