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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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