A four-digit house number contains no zeros. The number has exactly three distinct digits. How many such numbers are there?
A four-digit house number contains no zeros. The number has exactly three distinct digits. How many such numbers are there?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
A four-digit house number contains no zeros. The number has exactly three distinct digits. How many such numbers are there?
Expert Solution
Step 1
It is given that a four digit house number has no digits.
The number has exactly 3 distinct digits.
This implies that one of the three digits repeats.
The objective is to evaluate the number of possibilities.
The property of combinations is used to solve the problems.
The number of ways to choose objects from possibilities without repetition is .
The formula to evaluate is .
The number of ways to arrange objects in positions is .
The formula to evaluate is .
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