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 . . . . .❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤

## Answers ( )

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

➡️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.━━━━━━━━━━━━━━━━━━━━━━━━━