Combinatorics

# Mississipi has 4 dis5nct lexers misp with 1442

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Unformatted text preview: Thus, the number of permuta5ons with this paxern is P(5,5)=5! –  If we ﬁx the paxern bge, then we consider it as a single block. Thus, the number of permuta5ons with this paxern is P(5,5)=5! –  Fixing the paxer eaf, we have the same number: 5! –  Thus, we have (7! – 2.5!). Is this correct? –  No! we have subtracted too many permuta5ons: ones containing both eaf and bfe. CSCE 235 Combinatorics 33 Permuta5ons: Example C (2) –  There are two cases: (1) eaf comes ﬁrst, (2) bge comes ﬁrst –  Are there any cases where eaf comes before bge? –  No! The lexer e cannot be used twice –  If bge comes ﬁrst, then the paxern must be bgeaf, so we have 3 blocks or 3! arrangements –  Altogether, we have 7! – 2.(5!) + 3! = 4806 CSCE 235 Combinatorics 34 Outline •  Introduc5on •  Coun5ng:...
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