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Permutations-and-Combinations

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					                         Standards:
MM1D1b. Calculate and use simple permutations and combinations.




         Permutations
             and
         Combinations
              Lunch         Ice Cream Sundae
                                  Chocolate




                                  Strawberry




                                  Pineapple




                                   Caramel




How many different lunches could you order if
 there were 4 different sandwiches, 3 different
 side orders and 4 different drinks?

How many different ice cream sundaes could you
 order if there were 3 different flavors of ice
 cream, 4 different sauces, and 2 different
 toppings?
           Lunch       Ice Cream Sundae
                             Chocolate




                             Strawberry




                             Pineapple




                              Caramel




Suppose you wanted lunch and an ice
 cream sundae. What would you do?

Suppose you wanted either lunch or an ice
 cream sundae. What would you do?
 When using the        When using the
counting principle,   counting principle,
  the word “and”        the word “or”
means to multiply.      means to add.


       x                     +
                N factorial
For any positive integer n, the product of
   integers from 1 to n is called n factorial
   and is written as n!. The value of 0! Is
   defined to be 1.
Examples:
1. 5!
5·4·3·2·1=
2. 9!
9·8·7·6·5·4·3·2·1=
             Permutations
A permutation is an arrangement of objects
  in which order is important. The number
  of permutations of n objects is given by nPn
  = n!. The number of permutations of n
  objects taken r at a time, where r ≤ n, is
  given by nPr = n!
                 (n – r)!
Example 1
You Try!!
Example 2
You Try!!
Example 3
You Try!!
Guided Practice
                Guided Practice




Evaluate the expression.
8. 4P3                 9. 6P2     10. 7P4
             Homework

Math 1 Textbook:

         pg 344: 1 – 18 ALL

         write problems and show all work!!
            Combinations
A combination is a selection of objects in
  which order is NOT important. The
  number of combinations of n objects taken
  r at a time, where r ≤ n, is given by
                nC r =       n!
                        (n – r)! · r!
Example 1
Example 2
You Try!
Example 3
Example 3 cont…
You Try!
             Homework
pg 349: 1 – 20 ALL

         write problems and show all work!!

				
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