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Factorials

Factorials. Player A. Player B. Player C. C. B. A. B. C. C. A. B. A. C. A. B. C. B. A. Factorial Notation. Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be arranged.

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Factorials

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  1. Factorials

  2. Player A Player B Player C C B A B C C A B A C A B C B A Factorial Notation Allows us to represent, and quickly calculate, the number of different ways that a set of objects can be arranged. Ex: How many different ways can a coach organize the three chosen shooters to take part in a shootout in a hockey game. Resulting Order ABC Using our tree diagram concept… ACB BAC BCA So there are 6 ways to order the shooters CAB CBA

  3. Factorial Notation Ex: How many different ways can a coach organize the three chosen shooters to take part in a shootout in a hockey game. An easier way to calculate the number of possible ways to order the shooter is to think about the choices at each position. Shooter 1 Shooter 2 Shooter 3 3 choices 2 choices 1 choice 6 3 x 2 x 1 = So there are 6 ways to order the shooters

  4. Factorial Notation Factorial notation presents us with a method of easily representing the expression included on the last slide; 3 x 2 x 1 = 6 Written using factorial notation 3! Pronounced as “three factorial” Which means

  5. To multiply consecutive #’s we can use factorial notation. Eg. 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 8! Use your scientific calculator to solve! 8 N! 40320 = 40320 Find: 3!= 5! = 10! = 6 120 3,628,000 In general n! = n(n-1)(n-2)(n-3) . . . (3)(2)(1)

  6. Working with the Notation a) Simplify b) Simplify c) Express 10 x 9 x 8 x 7 as a factorial.

  7. The group Major Lazer has 12 songs they want to sing at their show on Friday night. How many different set lists can be made?

  8. 10 students are to be placed in a row for photos. Katie and Jake must be beside each other. How many arrangements are there? K and J

  9. How many arrangements have them NOT beside each other?

  10. Homework • Pg 239 #1, 2, 7, 9, 11,12,13

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