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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# The Fundamental Counting Principle

For Math Class

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