Do Now 4/28/11 Take out HW from last night. Take out HW from last night.  Text p. 617, #10-30 evens Copy HW in your planner. Copy HW in your planner.

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Do Now 4/28/11 Take out HW from last night. Take out HW from last night.  Text p. 617, #10-30 evens Copy HW in your planner. Copy HW in your planner.  Text p. 623, #12-22 evens, 23 – 26 all In your journal, answer the following question. A basketball league has 5 teams. Two of the teams are chosen to play one another. How many different possible matchups are there? In your journal, answer the following question. A basketball league has 5 teams. Two of the teams are chosen to play one another. How many different possible matchups are there?

Homework Text p. 617, #10-30 evens 10) 6 10) 6 12) 1 12) 1 14) 40,320 14) 40,320 16) 362,880 16) 362,880 18) ) ) 42 20) 42 22) ) ) ) ) 32,760 26) 32,760 28) 1/120 28) 1/120 30) 6 ways 30) 6 ways

Section 11.6 “Permutations” Permutation an arrangement of objects in which order is important. How many arrangements can you make with the letters A, B, and C?

The expression 3 · 2 · 1 can be written as 3! This is read as “3 factorial.” “3 factorial.” n Factorial n! = n · (n – 1) · (n – 2) · … · 1 6! = 3! = 3 · 2 · 1 = 6 6 · 5 · 4 · 3 · 2 · 1 = 720

Permutations ( of n objects taken r ) 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?

Section 11.7 “Combinations” Combination an arrangement of objects in which the order of the objects chosen is not important. A basketball league has 5 teams. Two of the teams are chosen to play one another. How many different possible matchups are there? A basketball league has 5 teams. Two of the teams are chosen to play one another. How many different possible matchups are there?

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?

nCr nCr Combinations Number of total objects Objects taken at a time 4 different combinations 4 different combinations Combinations ( of n objects taken r ) To use the nCr button, press the ‘PRB’ button and scroll over to the ‘nCr’ button. To solve the question, in your calculator type 4 then ‘PRB’ scroll over to ‘nCr’ then type 3. You want to buy 4 CDs. You can afford to buy only 3 of them. How many different combinations of CDs can you buy?

Permutation VS. Combination The order of the objects is important in the arrangement The order of the objects is not important it is the group that counts. Always more possibilitiesAlways less possibilities

Permutation OR Combination 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 blue ribbons? There are 30 runners in a cross country race. How many different groups of runners can finish 1st, 2nd, or 3rd? 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 different pairs of sculptors can receive prizes? There are 50 students in the Speech club. Three of these students will be chosen to represent the school at a competition. How many different groups of three students can be chosen? Combination Permutation Permutation Combination

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