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Combinatorics

# I r 2 while ai n ri do 3 i i 1 4 end

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Unformatted text preview: ≤ n is is read ‘n choose k’. \${n \choose k}\$ CSCE 235 Combinatorics 37 Combina5ons (3) •  A useful fact about combina5ons is that they are symmetric •  Corollary: Let n, k be nonnega5ve integers with k ≤ n, then CSCE 235 Combinatorics 38 Combina5ons: Example A •  In the Powerball loxery, you pick –  ﬁve numbers between 1 and 55 and –  A single ‘powerball’ number between 1 and 42 How many possible plays are there? •  Here order does not maxer –  The number of ways of choosing 5 numbers is –  There are 42 possible ways to choose the powerball –  The two events are not mutually exclusive: –  The odds of winning are CSCE 235 Combinatorics 39 Combina5ons: Example B •  In a sequence of 10...
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