# How Many Three-digit Numbers Are There with No Digit Repeated? - Mathematics

How many three-digit numbers are there with no digit repeated?

#### Solution

The thousand's place cannot be zero.
∴ Number of ways of selecting the thousand's digit = 9
Number of ways of selecting the ten's digit = 9 ( as repetition of digits is not allowed and one digit has already been used in the thousand's place)
Similarly, number of ways of selecting the unit's digit = 8 (as two digits have been used for the thousand's and the ten's places)
∴ Total three digit number that can be formed = 9$\times$9$\times$8 = 648

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.2 | Q 16 | Page 15

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