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Question:
how many 4-digit number are there with no digit repeated
Answer:

A four digit number is to be formed from the digits 0,1,2,3,4,5,6,7,8,9.
□□□□ T
hHTO
Since, leftmost place i.e thousand's place cannot have zero. So, there are 9 ways to fill thousand's place.
Since, repetition is not allowed , so hundreds place can be filled by remaining 9 digits .
So, hundred's place can be filled in 9 ways.
Similarly, to fill tens place, we have 8 digits remaining.
So,tens place can be filled by 8 ways.
Similarly, to fill ones place, we have 7 digits remaining.-->7 ways 
So, required number of ways in which four digit numbers can be formed from the given digits is 

9×9×8×7=4536

 

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