Counting Principles Addition Multiplication Counting Principles Addition Principle

Counting Principles Addition & Multiplication

Counting Principles �Addition Principle: �Multiplication �“OR” problems �“AND” problems �* if the outcomes are not �It’s the multiplication mutually exclusive, you have to subtract the overlapping elements* �It’s the addition principle, therefore, you ADD!!!! principle, therefore, you MULTIPLY!!!!

Multiplication �Example 1. If we flip a coin, say a penny, then the two possible outcomes are that the penny lands heads or that it lands tails. We designate these with the letters H and T. If we flip two coins, say now a penny and a nickel, find the number of possible outcomes.

Multiplication �Example 2. Next suppose we add a dime to the action, so that now we flip three coins. Find the number of possible outcomes.

Multiplication �Example 3. How many different license plates can be made by a state, if each plate is to display three letters followed by three numbers?

Multiplication �Example 4. Suppose a room has 5 lamps, each with an ordinary on-or-off bulb. The number of ways of lighting the room is ____.

Multiplication �Example 5. A dance class has 10 men and 12 women. How many ways can the dance instructor choose a couple to demonstrate the foxtrot at a charity ball?

Multiplication �Example 6. Next suppose the instructor may dress the woman in a long evening gown, a mid-length dress, or a miniskirt, and the man in a tuxedo or suit. How many ways can she choose and dress the couple?

Multiplication �* Example 7 *. How many different 3 -digit even numbers are there?

Addition �Angie will draw one card from a standard deck of playing cards. How many ways can she choose � �(a) a king or a queen? �(b) a king or a black card? �(c) an even number or a spade? �(d) a heart, a diamond, or a club?

Addition & Multiplication �A civics club consists of � 9 female Democrats � 5 male Democrats � 6 female Republicans � 7 male Republicans �How many ways can the club choose �(a) a female Democrat and a male Republican to serve on the budget committee? �(b) a female Democrat or a male Republican to serve as chairperson? �(c) a female or a Republican to serve as chairperson?

Addition & Multiplication �The state of California makes license plates with 3 letters followed by 3 numbers, and also plates with 3 numbers followed by 3 letters. How many different license plates are possible in California?