Q. 24.0( 125 Votes )

How many 4-digit numbers are there with no digit repeated?

Answer :

In questions like these we need to fill the places that are to be occupied.

To find: Four digit number (digits does not repeat)

Now we will have 4 places where 4 digits are to be put.


At thousand's place = There are 9 ways as 0 cannot be at thousand's place = 9 ways

At hundredth's place = There are 9 digits to be filled as 1 digit is already taken = 9 ways

At ten's place = There are now 8 digits to be filled as 2 digits are already taken = 8 ways

At unit's place = There are 7 digits that can be filled = 7 ways

Total Number of ways to fill the four places = 9 × 9 × 8 × 7 = 4536 ways.

So a total of 4536 four digit numbers can be there with no digits repeated.

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