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

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

#### Solution

Total number of 3-digit numbers = Number of arrangements of 10 numbers, taken 3 at a time = 10P3 =$\frac{10!}{7!} = 10 \times 9 \times 8 = 720$

Total number of 3-digit numbers, having 0 at its hundred's place = 9P2 =$\frac{9!}{7!} = 9 \times 8 = 72$

Total number of 3-digit numbers with distinct digits = 10P3$-$ 9P2 = 720$-$ 72 = 648

Concept: Factorial N (N!) Permutations and Combinations
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.3 | Q 25 | Page 29