# Permutations and Combinations Standards: MM1D1b. Calculate and use simple permutations and combinations

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• Permutations and CombinationsStandards:MM1D1b. Calculate and use simple permutations and combinations.

• 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?

• 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?

• N factorialFor 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:5!5 4 3 2 1 = 2. 9!9 8 7 6 5 4 3 2 1 =

• PermutationsA 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!!

• CombinationsA 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 nCr = n!(n r)! r!

• Example 1

• Example 2

• You Try!

• Example 3

• Example 3 cont

• You Try!

• Homeworkpg 349: 1 20 ALL

write problems and show all work!!

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