WARM-UP Evaluate each expression. 1.8!2.3. 9 P 5 14! 10!4! 40,320 1001 15,120.

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Presentation transcript:

WARM-UP Evaluate each expression. 1.8! P 5 14! 10!4! 40, ,120

Counting Techniques Combinations

Combination Counting technique in which order does NOT matter (i.e. CO is the same as OC). Written nCr n=# of choices r=arranged how many ways

Example 1: Combinations Evaluate 10 C C 4 = 10! 4!(10 – 4)! = 10! 4! 6! = //////////// //////////// = = 210

Example 2: Combinations Evaluate 12 C C 3 = 12! 3!(12 – 3)! = 12! 3! 9! 12*11* *8*7* = / / / / / / = = 220 / / / / / /

You Try!!! Evaluate 1)C(10,5) 252 2)C(8,2) 28 3)C(25,7) 480,700

Example 3 A reading list for a course in world literature has 20 books on it. In how many ways can you choose 4 books to read? n=20 books to choose from r= 4 books at a time Find C(20,4) = 4845

Example 4: Combinations A disk jockey wants to select 5 songs from a new CD that contains 12 songs. How many 5-song selections are possible? Relate: 12 songs chosen 5 songs at a time Define: Let n = total number of songs. Let r = number of songs chosen at a time. Write: n C r = 12 C 5 You can choose five songs in 792 ways. Use the n C r feature of your calculator.

YOU TRY!!! In this class we have 20 people. In how many ways can I select 6 students? 38760