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
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Chapter2: Second-order Linear Odes
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A four-digit house number contains no zeros. The number has exactly three distinct digits. How many such numbers are there?

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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 r objects from n possibilities without repetition is Crn.

The formula to evaluate Crn is Crn=n!r!·n-r!.

The number of ways to arrange n objects in r positions is Prn.

The formula to evaluate Prn is Prn=n!n-r!.

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