Do Now 4/28/11Do Now 4/28/11

Take out HW from last night.Take out HW from last night. Text p. 617, #10-30 evensText p. 617, #10-30 evens

Copy HW in your planner.Copy HW in your planner. Text p. 623, #12-22 evens, 23 – 26 allText p. 623, #12-22 evens, 23 – 26 all

In your journal, answer the following question. A In your journal, answer the following question. A basketball league has 5 teams. Two of the basketball league has 5 teams. Two of the teams are chosen to play one another. How teams are chosen to play one another. How many different possible matchups are there? many different possible matchups are there?

HomeworkHomework Text p. 617, #10-30 evens Text p. 617, #10-30 evens

10) 610) 6 12) 112) 1 14) 40,32014) 40,320 16) 362,88016) 362,880 18) 12018) 120

20) 4220) 42 22) 72022) 720 24) 60024) 600 26) 32,76026) 32,760 28) 1/12028) 1/120 30) 6 ways30) 6 ways

Section 11.6 “Permutations”Section 11.6 “Permutations”

PermutationPermutationan arrangement of objects in which order is important.

How many arrangements can you make with the letters A, B, and C?

The expression The expression 3 · 2 · 1 3 · 2 · 1 can be written as can be written as 3! 3! This is read asThis is read as “ “3 factorial.” 3 factorial.”

n Factorialn Factorial

n! = n · (n – 1) · (n – 2) · … · 1n! = n · (n – 1) · (n – 2) · … · 1

6! =6! =

3! = 3 · 2 · 1 = 63! = 3 · 2 · 1 = 6

6 · 5 · 4 · 3 · 2 · 1 = 7206 · 5 · 4 · 3 · 2 · 1 = 720

PermutationsPermutations ((of of nn objects taken objects taken rr ) )

You have 7 posters and want to chose 4 of them, one for each wall in your room. How many

different arrangements of posters are possible?

rn p !3

!7

)!47(

!7

123

1234567

8404567

Section 11.7 “Combinations”Section 11.7 “Combinations”

CombinationCombinationan arrangement of objects in which an arrangement of objects in which the order of the objects chosen is the order of the objects chosen is not important.not important.

rnC !r

Prn

A basketball league has 5 A basketball league has 5 teams. Two of the teams are teams. Two of the teams are chosen to play one another. How chosen to play one another. How many different possible matchups many different possible matchups are there?are there?

12

45

!2!3!5

)!25(!5

10

2

20

Combinations (of n objects taken r )

You need to read 4 books for summer reading. Your teacher gives you a list of 7 books from

which to choose. How many different groups of 4 books can you choose?

rnC !r

Prn

1234

456735

24

840

nCrnCrCombinationsCombinationsNumber of Number of

total objectstotal objects

Objects taken Objects taken at a timeat a time

4 different combinations4 different combinations

CombinationsCombinations ((of of nn objects taken objects taken rr ) )

To use the nCr button, press the ‘PRB’ button and scroll over To use the nCr button, press the ‘PRB’ button and scroll over to the ‘nCr’ button. to the ‘nCr’ button.

To solve the question, in your calculator type 4 then ‘PRB’ To solve the question, in your calculator type 4 then ‘PRB’ scroll over to ‘nCr’ then type 3.scroll over to ‘nCr’ then type 3.

You want to buy 4 CDs. You want to buy 4 CDs. You can afford to buy You can afford to buy only 3 of them. How only 3 of them. How many different many different combinations of CDs can combinations of CDs can you buy?you buy?

Permutation VS. CombinationPermutation VS. Combination

The order of the objects The order of the objects is important in the is important in the

arrangementarrangement

rn p

The order of the objects The order of the objects is not important it is is not important it is

the group that counts.the group that counts.

rnC

Always more possibilities Always less possibilities

Permutation OR CombinationPermutation OR Combination There are 30 dogs in a dog show. Blue ribbons are awarded to There are 30 dogs in a dog show. Blue ribbons are awarded to the top 3 dogs. How many different groups of dogs can receive the top 3 dogs. How many different groups of dogs can receive blue ribbons? blue ribbons?

There are 30 runners in a cross country race. How many There are 30 runners in a cross country race. How many different groups of runners can finish 1different groups of runners can finish 1stst, 2, 2ndnd, or 3, or 3rdrd? ?

There are 50 sculptures in an art show. A Best-in-Show prize There are 50 sculptures in an art show. A Best-in-Show prize and runner-up prize are awarded to the top 2 scholars. How many and runner-up prize are awarded to the top 2 scholars. How many different pairs of sculptors can receive prizes? different pairs of sculptors can receive prizes?

There are 50 students in the Speech club. Three of these There are 50 students in the Speech club. Three of these students will be chosen to represent the school at a competition. students will be chosen to represent the school at a competition. How many different groups of three students can be chosen? How many different groups of three students can be chosen?

CombinationCombination

PermutationPermutation

PermutationPermutation

CombinationCombination

Homework

Text p. 623, #12-22 evens, 23 – 26 allText p. 623, #12-22 evens, 23 – 26 all