Combinatorics

# With indisnguishable objects algorithms genera5ng

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Unformatted text preview: 8.6 page 562 CSCE 235 Combinatorics 30 Permuta5ons: Example A •  How many pairs of dance partners can be selected from a group of 12 women and 20 men? –  The ﬁrst woman can partner with any of the 20 men, the second with any of the remaining 19, etc. –  To partner all 12 women, we have P(20,12) = 20!/8! = 9.10.11…20 CSCE 235 Combinatorics 31 Permuta5ons: Example B •  In how many ways can the English lexers be arranged so that there are exactly 10 lexers between a and z? –  The number of ways is P(24,10) –  Since we can choose either a or z to come ﬁrst, then there are 2P(24,10) arrangements of the 12- lexer block –  For the remaining 14 lexers, there are P(15,15)=15! possible arrangements –  In all there are 2P(24,10).15! arrangements CSCE 235 Combinatorics 32 Permuta5ons: Example C (1) •  How many permuta5ons of the lexers a, b, c, d, e, f, g contain neither the paxern bge nor eaf? –  The total number of permuta5ons is P(7,7)=7! –  If we ﬁx the paxern bge, then we consider it as a single block....
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