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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.
 Spring '08
 STAFF

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