Combinatorics

Boxes then there is at least one box containing two

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Unformatted text preview: = 162 CSCE 235 Combinatorics 13 Applica5on of PIE: Example A (3) •  How many integers between 1 and 300 (inclusive) are divisible by 3 and by 5 but not by 7? Answer: |(A ∩ B)\C| •  By the defini5on of set- minus |(A ∩ B)\C| = |A ∩ B| - |A ∩ B ∩ C| = 20 – 2 = 18 Knowing that |A| = ⎣ྏ300/3⎦ྏ = 100 |A∩B| = ⎣ྏ300/15⎦ྏ = 20 |B| = ⎣ྏ300/5⎦ྏ = 60 |A∩C| = ⎣ྏ300/21⎦ྏ = 100 |C| = ⎣ྏ300/7⎦ྏ = 42 |B∩C| = ⎣ྏ300/35⎦ྏ = 8 |A∩B∩C| = ⎣ྏ300/105⎦ྏ = 2 •  CSCE 235 Combinatorics 14 Applica5on of PIE: Example A (4) •  How many integers between 1 and 300 (inclusive) are divisible by 5 but by...
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This note was uploaded on 10/31/2013 for the course CSCE 235 taught by Professor Staff during the Spring '08 term at UNL.

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