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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 Spring '08
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