# Mathematics 1228A/B Lecture 1: Section 1.3 Sep 18, 2019

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Published on 2 Aug 2020

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Department

Course

Professor

The Fundamental Counting Principle!

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Theorem:!

"If there are k decision to be made, with Mi choices available for the ith decision, for i =1...k!

No matter which choice is selected at some earlier decision, then the number of diﬀerent ways of making all k decisions is m1

x m2 x ....mk!

!

!

Suppose there’s !

3 diﬀerent burger and !

4 kinds of soft drink and !

3 choices of side orders and !

3 diﬀerent sizes!

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The # of ways to decide is 3x4x2x3=72 ways!

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Example 1.6!

How many 3 digit codes can be formed from the digits 0-9!

"i) if repetition of digits within the code is allowed?!

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"ii) if repetition is not allowed!

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How many 3 digits codes can be formed if repetition is not allowed and the code must either start with an odd digit or else

must contain only even digits.!

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Example 1.7!

"How many 3 digit codes have at least one repeated digits?!

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Example 1.8!

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1) How many subset of {a,b} are there?!

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2) How many subset of {a,b,c} are there!

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3) How many subset of (a, b, c, d, e, f) are there!

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4) How many subset of {a, b,c,d,e,f} are there which contain the d but have no vowels.!

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Theorem:!

A set containing n element has 2^n subsets

10 10 10 1000

10 98720

59872 5360

54360

1420710

1010 1000 possible

no rep 10 98e720

at least Irepeat tooo 220 280

0alb lab

0AibCab Ac bc iAbc

2Choicesfora2choicesfor b2choicesfo cIn Out

23

26 2222x22

dxz

abC

11 I

## Document Summary

No matter which choice is selected at some earlier decision, then the number of di erent ways of making all k decisions is m1 x m2 x mk. If there are k decision to be made, with mi choices available for the ith decision, for i =1k. The # of ways to decide is 3x4x2x3=72 ways. How many 3 digit codes can be formed from the digits 0-9: if repetition of digits within the code is allowed, if repetition is not allowed. How many 3 digits codes can be formed if repetition is not allowed and the code must either start with an odd digit or else must contain only even digits. 1010 1000 possible no rep 10 9 8 e 720 at least i repeat tooo 220 280. Example 1. 8: how many subset of {a,b} are there, how many subset of {a,b,c} are there. 0 a i b c ab ac bc i abc.