How many 3-digit numbers with digits in {1,..., 9} (repeats allowed) are divisible by 9?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
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.
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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,