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
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
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