Mathematics 1228A/B Lecture Notes - Lecture 1: Hercule Poirot, Dionne Quintuplets, Bobbsey Twins

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Published on 2 Aug 2020
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1.4 Permutations!
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A permutation of a set of objects is an arrangement, or an ordering, of the objects!
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Example 1.9!
In how many dierent ways can 5 distinct salads be arranged in a row on a buet table.!
5 positions ina line = 5 decisions. 5x4x3x2x1=120!
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For any integer n>=1, n!!
Pronouced n factorial,!
Is the product of the integers from n down to 1. Ex. 5!=5x4x3x2x1=120!
0!=1!
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Theorem:!
The number of permutation of n distinct objectes is n!!
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Example1.10!
2 dierent pasta salads and 3 dierent green salads are to be arranged in a row on a buet table.!
A) in how many ways can the salads be arranged so that pasta salads and green salads alternate!
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B) in how many ways can the salads be arranged if the 2 pasta salads must be side be side.!
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Example 1.11!
The Bobbsey Twins are actually 2 pairs of twins (two children born at the same time) in the same family. The Dionne
quintuplets are a set of 5 girls all born at the same time. these 9 people are going to be arranged in a line.!
A) in how many dierent ways can they be arranged if all siblings must be grouped together?!
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B) in how many dierent ways can they be arranged so that each of the bobbseys is beside his/her twin?!
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C) how many of the ways counted in b) have the 5 Dionnes all grouped together?!
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Example 1.12!
At a fund-raising dinner there are 4 dierent autographed books which will be given as door prizes. !
If 25 people attend the dinner, in how many dierent ways can the door prizes be awarded?!
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Greenhastogo fist
because ifpastawentfirst wewill run out Gp
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How
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t
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25 ways canbegiven 4waysthe book isgiven out 4
25 24 23 22
or 25 121
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Document Summary

A permutation of a set of objects is an arrangement, or an ordering, of the objects. In how many di erent ways can 5 distinct salads be arranged in a row on a bu et table. Is the product of the integers from n down to 1. The number of permutation of n distinct objectes is n! 2 di erent pasta salads and 3 di erent green salads are to be arranged in a row on a bu et table: in how many ways can the salads be arranged so that pasta salads and green salads alternate. Orderofgreens 3types 3 choices ofways tomake all 3decisions. 1 3121: in how many ways can the salads be arranged if the 2 pasta salads must be side be side. How many 3 diffgreen salad and a pairofps arrange. The bobbsey twins are actually 2 pairs of twins (two children born at the same time) in the same family.

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