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Counting Principles Addition & Multiplication

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

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Counting Principles Addition & Multiplication

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  1. Counting PrinciplesAddition & Multiplication

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

  3. 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.

  4. 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.

  5. 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?

  6. 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 ________.

  7. 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?

  8. 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?

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

  10. 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?

  11. 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?

  12. 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?

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