M119Notes2 - (Lesson 13: Counting; 4-6) 4.25 LESSON 13:...

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(Lesson 13: Counting; 4-6) 4.25 LESSON 13: COUNTING (SECTION 4-6) PART A: FUNDAMENTAL COUNTING RULE Let’s say there are two decisions to be made: Decision A and Decision B . If there are m possible choices for Decision A A 1 , A 2 , , A m ( ) and n possible choices for Decision B B 1 , B 2 , , B n ( ) , regardless of how A is decided, then there are mn possible ways to decide both A and B . Envision a possibility tree or a grid: A \ B B 1 B 2 B n A 1 A 2 A m This multiplication rule extends to more than two decisions.
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(Lesson 13: Counting; 4-6) 4.26 Example 1 Assume that a password must have the following characteristics: • It must be (exactly) four characters long. • It must begin with an uppercase letter. • Each of the other characters can be an uppercase letter or a digit from 0 to 9. How many possible passwords are there? Solution to Example 1 There are 26 possibilities (the uppercase letters) for the first character. There are 36 possibilities (the uppercase letters and the digits 0-9) for each of the others. The number of possible passwords is: 26 × 36 × 36 × 36 = 1,213,056 1 st 2 nd 3 rd 4 th Note: If you write 26 36 3 , remember that exponentiation precedes multiplication in the order of operations. Example 2 (Follow-Up) If a password is randomly selected, what is the probability that it is “IH8U”? Solution to Example 2
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This note was uploaded on 09/08/2011 for the course MATH 119 taught by Professor Staff during the Spring '11 term at Mesa CC.

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M119Notes2 - (Lesson 13: Counting; 4-6) 4.25 LESSON 13:...

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