1313Day15 - Math 1313 Section 5.3 Section 5.3 Generalized...

Math 1313 Section 5.3
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Section 5.3 Generalized Multiplication Principle
Suppose a task T
1
can be performed in N
1
ways, a task T
2
can be performed in N
2
ways,…, and , finally
a task T
n
can be performed in N
n
ways. Then the number of ways of performing the tasks T
1
, T
2
, …, T
n
in succession is given by the product
N
1
• N
2
•… •N
n
Example 1: A coin is tossed 3 times, and the sequence of heads and tails is recorded.
a. Determine the number of outcomes of this activity.
b. List the outcomes of this experiment by first drawing a tree diagram.
Example 2: The Burger Bar offers the following items on its menu:
Burger Sides Beverages Desserts
Single Meat Fries Tea Cheesecake
Double Meat Onion Rings Coffee Brownie
Fruit Bowl Soda Cookie
Cheddar Peppers Ice Cream Cone
If a customer chooses 1 item from each category, how many meals can be made? List 1 meal possible.

Math 1313 Section 5.3
2
Example 3: An identification number for employees at a certain company contains six digits. How
many ID numbers are possible if repetition is allowed?
Example 4: A license plate consists of 2 letters followed by 4 digits. How many license plates are
possible if the 1st letter can't be O, the 1st digit can't be 0 and no repetitions are allowed?
Example 5: In the original plan for area codes in 1945, the first digit could be any number from 2
through 9, the second digit was either 0 or 1, and the third digit could be any number except 0. With this
plan, how many different area codes were possible?
Popper 5: