Discrete maths Rosen Counting

Question

How many strings of four decimal digits do not contain the same digit twice?

Comments

does 0000 to 0999also count as 4 decimal digits ?

Answer 1

The first digit may be any of the ten digits. 
The second may be any of the nine remaining. 
The third may be any of the eight not yet used. 
The fourth may be any of the seven not yet used. 

So, there are 10 × 9 × 8 × 7 = 5040 

Comments

so we do consider 0 in the MSB place. Was getting a doubt in that

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Even i have doubt about that but in the question they just have mentioned "strings of four decimal digits do not contain the same digit twice"

so i assumed they are not talking about a 4 digit number rather strings of 4 digits