Question

How many four - digit numbers there in all?​

Answer 1

Step-by-step explanation

4 digit number from - 9999 and - 1000

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Answer 2

Answer:

Well to simplify it , lets consider the Number of places and lets try to figure out what are the possible numbers that can be assigned in each place to make a valid 4 digit number.

For starters lets remember there are 10 possible numerals that can be filled in each space i.e 0,1,2,3,4,5,6,7,8 and 9

So the 4 digit number will be formed as _ _ _ _

Now, the first place cant have 0 as a number (as it would become a 3 digit number then), so the remaining 9 numbers can be filled in the 1st place

so 9 _ _ _

For the next 3 blanks , each blank can have any of the 10 digits, so the possible no of permutations become

9*10*10*10 = 9000. So there are 9000 4 digit numbers

If the condition were such such that no Digit could be repeated , then

As usual, the first place would have 9 options(since 0 cant be used),

The second place would have 9 options( since the digit used in the fist place out of the 10 digits cant be used)

The third place would have 8 options(excluding the digits in the 1st and 2nd place)

the fourth place would have just 7 options left

So the total number of 4 digits with no repeat would be 9*9*8*7 = 4536 numbers.

Hope this helps :)