Question

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

Answer 1

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

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➡️To find four digit number (digits does not repeat)

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

➡️So, 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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Answer 2

There are 4537 four digit-numbers with no digit repeated.
Explanation :
So we have 10 numbers, which are 0,1,2,3,4,5,6,7,8,9.
And we have to make four digit numbers with no reputation.
So we have four places which are THOUSANDS - HUNDREDS - TENS - ONES, for ONES place we have 7 ways of filling numbers ; for TENS place we have 8 options left; for HUNDREDS place we have 9 options ; for THOUSANDS we have 9 options left.
By the PRINCIPLE OF COUNTING,

When there are m ways to do one thing,
and n ways to do another,
then there are m×n ways of doing both.

So, we have four ways which are 9*9*8*7, on multiplying, we will get our answer which is 4537
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