Concept explainers
To calculate: The number of multiples of 3 less than 100 with digits 1, 4, 5, 7 and 8.
Answer to Problem 15WE
The number of multiples of 3 less than 100 with digits 1, 4, 5, 7 and 8 are
Explanation of Solution
Given information:
The number of multiples of 3 less than 100 with digits 1, 4, 5, 7 and 8 are to be formed.
Formula used:
Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are
Calculation:
Consider the provided information that number of multiples of 3 less than 100 with digits 1, 4, 5, 7 and 8 are to be formed.
A number is a multiple of 3 if the sum of digits is a multiple of 3.
From the provided digits no single digit multiple of 3 is there.
Let 2-digit numberbe
If 1 is fixed at ten’s digit then possible numbers at one’s digit are 5 and 8 since sum of digits of 15 and 18 add up to multiple of 3 that is 6 and 9 respectively.
So, numbers that are multiple of 3 are 15, 18, 51 and 81.
If 4 is fixed at ten’s digit then possible numbers at one’s digit are 5 and 8 since sum of digits of 45 and 48 add up to multiple of 3 that is 9 and 12 respectively.
So, numbers that are multiple of 3 are 45, 48, 54 and 84.
If 5 is fixed at ten’s digit then possible numbers at one’s digit are 1, 4 and 7 since sum of digits of 15, 54 and 57 add up to multiple of 3 that is 6, 9 and 12 respectively.
So, numbers that are multiple of 3 are 57 and 75. Rest are already obtained above.
If 7 is fixed at ten’s digit then possible numbers at one’s digit are 5 and 8 since sum of digits of 75 and 78 add up to multiple of 3 that is 12 and 15 respectively.
So, numbers that are multiple of 3 are 78 and 87. Rest are already obtained above.
Count the number of multiples of 3 obtained above.
The count is 12.
Thus, number of multiples of 3 less than 100 with digits 1, 4, 5, 7 and 8 are
Chapter 15 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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