(a) Use the technique shown in Example 9.1.4 to find the number of positive three-digit integers that are multiples of 6. The smallest positive three-digit integer that is a multiple of 6 is 6 · The...

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Extracted text: (a) Use the technique shown in Example 9.1.4 to find the number of positive three-digit integers that are multiples of 6. The smallest positive three-digit integer that is a multiple of 6 is 6 · The largest positive three-digit integer that is a multiple of 6 is 6 · Therefore, the number of three-digit integers that are multiples of 6 is (b) What is the probability that a randomly chosen positive three-digit integer is a multiple of 6? (c) What is the probability that a randomly chosen positive three-digit integer is a multiple of 7?


Extracted text: Example 9.1.4 Counting the Elements of a Sublist a. How many three-digit integers (integers from 100 to 999 inclusive) are divisible by 5? b. What is the probability that a randomly chosen three-digit integer is divisible by 5? Solution a. Imagine writing the three-digit integers in a row, noting those that are multiples of 5 and drawing arrows between each such integer and its corresponding multiple of 5. 100 101 102 103 104 105 106 107 108 109 110 994 995 996 997 998 999 5-20 5-21 5.22 5.199 From the sketch it is clear that there are as many three-digit integers that are mul- tiples of 5 as there are integers from 20 to 199 inclusive. By Theorem 9.1.1, there are 199 - 20+ 1, or 180, such integers. Hence there are 180 three-digit integers that are divisible by 5. and b. By Theorem 9.1.1 the total number of integers from 100 through 999 is 999 – 100+1 = 900. By part (a), 180 of these are divisible by 5. Hence the probability that a randomly chosen three-digit integer is divisible by 5 is 180/900 = 1/5.