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6.7 Day 2 Combinations 2011
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January 31, 2011
6.7 Day 2Combinations
Objective: Review permutations and count combinations.
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Warmup:1. In how many ways can you arrange 6 plants on a shelf?
2. In how many ways can 10 dogs line up to be groomed?
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ReviewnPr = n!(n r)!
Permutation: An arrangement of items in a particular order.
Example #1: 6P3 METHOD 1 METHOD 2 (Formula) (Counting Principle)
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Example #2: Seven yachts enter a race. First, second, and third place trophies will be given to the three fastest yachts. How many arrangements of first, second, and third places are possible with seven yachts?
There are 210 possible arrangements.
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Divide by r! to cancel the repeats.
nCr = n!r!(n r)!
Combination: Any unordered selection of r objects from a set of n objects.
COMBINATIONS
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nCr = n!r!(n r)!
COMBINATIONS
Example #3: 7C4 METHOD 1 METHOD 2 (Formula) (Shortcut)
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Example #4: Evaluate each expression.
a. 10C5 b. 8C2 c. 25C7
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Example #5: A reading list for a course in world literature contains 20 books. In how many ways can you choose four books to read?
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Example #6: Ten candidates are running for three seats in the student council. You may vote for as many as three candidates. In how many ways can you vote for three or fewer candidates?
10C3 + 10C2 + 10C1 + 10C0
Challenge
120 + 45 + 10 + 1 = 176 ways
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Homework:page 348
(21 32, 40, 46 49, 64)
