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How many 3-digit numbers are there with no digit repeated?

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Given: We have 10 numbers i.e. 0,1,2,3,4,5,6,7,8,9 

To Find: Number of 3-digit numbers formed with no repetition of digits. 

Conditions: No digit is repeated 

Let us represent the 3-digit number

First place can be filled with 9 numbers, i.e. 1,2,3,4,5,6,7,8,9 (0 cannot be placed as it will make it a 2-digit number) = 9 ways 

Second place can be filled with remaining 9 numbers (as one number is used already) = 9 ways 

Similarly, third place can be filled with 8 numbers = 8 ways 

Total number of 3-digit numbers which can be formed 

= 9 × 9 × 8 = 648

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