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Question
Count the numbers between 999 and 10000 subject to the condition that there are no digit is repeated
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Solution
Since 0 is given as a digit
We have to start filling 1000’s place.
Now 1000’s place can be filled in 9 ways (excluding 0)
Then the 100’s place can be filled in 9 ways (excluding one digit and including 0)
10’s place can be filled in (9 – 1)8 ways and unit place can be filled in (8 – 1)7 ways
So the number of 4 digit numbers are 9 × 9 × 8 × 7 = 4536 ways
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