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

Question:

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

 

Solution:

In forming a 3 digit number the 100 's place can be occupied by any 9 out of 10 digits (0 not included because it will lead to formation of 2 digit number.)

 

The 10 's place can be occupied by any of the remaining 9 digits (here 0 can or cannot be used.)

In one's place any of the remain 8 digits can be used.

So total 3-digit numbers with no digit repeated are: $9 \times 9 \times 8=648$.

 

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