How many numbers are there between 100 and 1000 in which all the digits are distinct?

Asked by Topperlearning User | 12th Sep, 2016, 11:52: PM

Expert Answer:

We know that a number between 100 and 1000 has three digits. 
So we have to find all the three digit numbers with distinct digits.

We cannot have 0 at the hundred’s place for 3-digit number.  So the hundred’s place can be filled with any of the 9 digits.  1,2,3,…..9.  So, there are 9 ways of filling the hundred’s place.

 

Now, 9 digits are left including 0.  So ten’s place can be filled with any of the remaining 9 digits in 9 was.  Now the unit’s place can be filled with any of the remaining 8 digits.  So, there are 8 ways of filling the unit’s place.

 

Hence, the total number of required numbers = 9 x 9 x 8= 648.

Answered by  | 13th Sep, 2016, 01:52: AM