Tree Diagrams 12-5

The counting principle If you are performing two experiments, where the first can be performed m ways and the second can be performed n ways, then the two experiments can be performed in m×n ways.
Example: Toss a coin followed by rolling a 6 sided die. 2 × 6 = 12
Draw the tree diagram.
With replacement/without replacement - If you perform the experiments on the same data, the experiment will change if you do or do not put the item back.
Example: Problem 10
If I pick up a die at random, put it down and pick up another, what is the
P(an event happening once) = 1-P(the event does not happen)

Counting Principle and Permutations

how many usernames can we make if we use two letters and 4 digits.
- With replacement
- 10 10 26 26 26 26
- Without replacement.
- 10 9 26 25 24 23 22
A permutation is an ordered arrangement of a set of objects.
How many ways can you arrange my 4 dice?
- 4×3×2×1
n! (n factorial), n! = n×(n-1)×(n-2) ··· 2×1
How many ways can I arrange 2 of my 4 dice: 4×3
this is written ₄P₂ read four permuted two ways.
_nP_r = n!/(n-r)!
You have an _nP_r button on your calculator.
₈P₂ = 8!/(8-2)! = 8!/6! = 8×7×6!/6!
Do problem 28 page 800
Do problem 36 page 800
Do problem 52 page 801