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Dicrete Maths Lectures - Discrete Mathematics Dr Fred...

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Discrete Mathematics Dr. Fred Phelps Lecture 1 Counting and Set Theory
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Announcements Please register for discrete math on the site http://dl.iitu.kz. The main textbook is on that site. The syllabus is also on that site. And a copy of the main textbook: Discrete Mathematics” by Lovasz, Pelikan and Veztergombi.
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LPV 1.1 Counting Problems from a Birthday Party Alice (♀) has a birthday party. Invites Bob (♂), Carl (♂), Diane (♀), Eve (♀), Frank (♂), George (♂) Total 7 people – four boys, three girls
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LPV 1.1 Counting Problems from a Birthday Party Problem 1 - Handshakes Everyone shakes everyone else’s hand. How many handshakes does this make? 7 people each shake 6 hands so 7·6=42. But, each handshake was double counted 7 6 21. 2 × =
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LPV 1.1 Counting Problems from a Birthday Party Problem 2 – Seating Arrangements How many ways can the guests be seated at the seven chairs at the table if Alice (the birthday girl) stays at the head of the table? Alice’s chair is fixed – only one possibility. Any one of six people (anyone besides Alice) can sit in the next (2nd) chair – six possibilities. Any one of five (anyone besides Alice or the occupant of the first chair) can sit in the third chair – five possibilities. And so on.
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LPV 1.1 Counting Problems from a Birthday Party Problem 2 – Seating Arrangements And so the total number of possible seating arrangements is: 1·6·5·4·3·2·1=6!=720.
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LPV 1.1 Counting Problems from a Birthday Party Problem 3 – Dance Pairings How many different sets of dancing pairs (boys dance with girls only) can be formed from the 4 boys and 3 girls? The textbook says this is easy. But the textbook’s solution is wrong! Notice that one boy will not have a partner. So lets start with the girls.
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LPV 1.1 Counting Problems from a Birthday Party Problem 3 – Dance Pairings 1st girl has four choices of partner 2nd girl has three choices 3rd girl has two choices So the number of possible dance pairs = 4x3x2=24.
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LPV 1.1 Counting Problems from a Birthday Party Problem 3 – Dance Pairings Now let’s try to solve this starting with the boys.
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