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The Fundamental Counting Principle

For Math Class
by

Cassandra Weekly

on 8 December 2010

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Transcript of The Fundamental Counting Principle

The Fundamental Counting Principle Cards
52 in a deck
4 in your hand
Card 1 - 52 options
Card 2 - 51 options
Card 3 - 50 options
Card 4 - 49 options 52 x 51 x 50 x 49 6497400 To chose one of these {a,b,c} AND to chose one of these {x,y}

Is to chose one of these {ax,bx,cx,ay,by,cy} Hi Mom By Cassandra By Cassandra Weekly
MTH 151-84

-Rebecca Eller- License Plates
3 letters (26 options each)
4 numbers (10 options each) Letter 1 - 26 options
Letter 2 - 26 options
Letter 3 - 26 options
Number 1 - 10 options
Number 2 - 10 options
Number 3 - 10 options
Number 4 - 10 options 26 x 26 x 26 x 10 x 10 x 10 x 10
or
26^3 x 10^4 175760000 Problem 1
How many two digit numbers are there? Problems Problem 2
Aaron, Becca, Chuck, and Dan (A, B, C, and D) are to seat themselves in four adjacent seats (1, 2, 3, and 4) so that A and B are beside each other. How many options do they have? Factorials 0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
8! = 40320
9! = 362880
10!= 3628800 For any counting number n factorial is given by

n! = n(n - 1)(n - 2)...2 x 1 4! = 4 x 3 x 2 x 1 Problem 3
6! - 3! Problem 4
Lynn Smith is taking thirteen preschoolers to the park. How many ways can the children line up, in single file? First number (1-9) = 9 options
Second number (0-9)= 10 options

9 x 10 = 90

[99 - 10 + 1 = 90] A and B have 3 choices for where to sit (1 and 2, 2 and 3, 3 and 4)
A and B have 2 choices for which side to sit on (A left, or B left)
C and D have 2 choices for which side to sit on (C left, or D left)

First option = 3 choices
Second option= 2 choices
Thrid option = 2 choices

3 x 2 x 2 = 12

6 x 5 x 4 x 3 x 2 x1 = 720
3 x 2 x 1 = 6

720 - 6 = 714 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 6227020800
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