How many 6-digit positive integers are divisible by 3 but not by 9 or by 10?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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How many 6-digit positive integers are divisible by 3 but not by 9 or by 10?

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Step 1

Sol:-

For a number to be divisible by 3, the sum of its digits must be divisible by 3. Let's consider the following cases:

Case 1: The first digit is not 1.

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