Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
**Problem Statement:** How many 3-digit numbers with digits in the set {1, ..., 9} (repeats allowed) are divisible by 9? **Explanation:** To solve this problem, we need to find the number of combinations of 3-digit numbers using the digits from 1 to 9 where the sum of the digits is divisible by 9. Repeated digits are allowed, meaning each digit from 1 to 9 can be used more than once in forming the numbers. The task involves considering the rule of divisibility by 9, which states that a number is divisible by 9 if the sum of its digits is also divisible by 9.
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Transcribed Image Text:**Problem Statement:** How many 3-digit numbers with digits in the set {1, ..., 9} (repeats allowed) are divisible by 9? **Explanation:** To solve this problem, we need to find the number of combinations of 3-digit numbers using the digits from 1 to 9 where the sum of the digits is divisible by 9. Repeated digits are allowed, meaning each digit from 1 to 9 can be used more than once in forming the numbers. The task involves considering the rule of divisibility by 9, which states that a number is divisible by 9 if the sum of its digits is also divisible by 9.
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