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Section 11.3: Combinations
(Objectives 1 ­ 2)
Recall: A permutation is any ordered arrangement of a given set of objects.
ex. A coach must choose a batting order of 9 players. He has 15 players to choose from. How many batting orders are possible?
ex. A coach must choose a team of 9 players. He has 15 players to choose from. How many teams are possible?
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Combination: a distinct set of items without regard to their order (no repetition allowed).
ex. There are 10 items on my "Things to Do" list. I only have time to do 3 of them today. How many options do I have in choosing the items I'll do today?
Ex. Lotto brochures formerly read:
"Lotto is the Florida Lottery game in which you could win millions of dollars by picking 6 numbers from 1 through 49."
How many possible 6­number picks were there?
Today's Lotto allows picking 6 numbers from 1 through 53. How many possible 6­number picks are there now?
22957480
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Distinguishing Between Permutations and Combinations
For each of the following examples, decide if it is a permutation or a combination problem.
ex. A club consists of 12 members. In how many ways can the club elect a president, a vice president, and a treasurer?
ex. "Pies Galore" features 8 kinds of pie every day. I only have enough money to buy 2 pies and I want to try 2 different kinds. How many options do I have?
ex. How many different six­member committees could be formed from the 100 U.S. senators?
ex. An employment agency has listed 5 highly skilled workers. In how many ways can 2 of these workers be selected if the 1st one chosen serves as foreman and the 2nd one chosen is the assistant?
ex. An employment agency has listed 5 highly skilled workers. In how many ways can 2 of these workers be selected to go to a conference?
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Using Combinations or Permutations with FCP
ex. Kristen went to the Party Store to buy 3 kinds of party favors and 6 kinds of game prizes for her birthday party. If there are 8 kinds of party favors and 10 kinds of game prizes to choose from, how many options does Kristen have?
ex. A Congressional committee consists of 4 senators and 6 representatives. A delegation of 5 members is to be chosen. How many delegations can be formed?
How many delegations can be formed if the delegation must include exactly 3 senators and 2 representatives?
How many delegations can be formed of senators only?
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ex. How many three­member committees consisting of all women can be formed from a group of 4 men and 5 women?
See text ex. 1 ­ 4. Use Counting Methods Handout in the packet.
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