Combinatorics

There are n possibili5es we have n people we are not

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Unformatted text preview: |A∩B∩C| = ⎣ྏ300/105⎦ྏ = 2 •  CSCE 235 Combinatorics 15 Applica5on of PIE: #Surjec5ons (Sec5on 7.6) •  The principle of inclusion- exclusion can be used to count the number of onto (surjec5ve) func5ons •  Theorem: Let A, B be non- empty sets of cardinality m,n with m≥n. Then there are ${n \choose i}$ See textbook, Sec+on 8.6 page 561 CSCE 235 Combinatorics 16 #Surjec5ons: Example •  How many ways of giving out 6 pieces of candy to 3 children if each child must receive at least one piece? •  This problem can be modeled as follows: –  Let A...
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