Question

How many numbers in the range 10000 to 99999 has no repeatz digit?

Answer 1

Answer:

89999

..........................

Answer 2

Between 10000 and 99999 (inclusive), there are 90000 numbers.

Let's try to find out, how many numbers do not contain 5.

Here, all are 5 digit numbers. If a number does not contain 5, then its digits are the different combinations of 0,1,2,3,4,6,7,8,9 (9 digits). Try to find out how many such combinations are possible. But here point is to remember that the 1st digit can’t be zero.

1st digit - 1,2,3,4,6,7,8,9 (8 digit) (any digit from these 8)

2nd digit - 0,1,2,3,4,6,7,8,9 (9 digit) (any digit from these 9)

3rd digit - 0,1,2,3,4,6,7,8,9 (9 digit) (any digit from these 9)

4th digit - 0,1,2,3,4,6,7,8,9 (9 digit) (any digit from these 9)

5th digit - 0,1,2,3,4,6,7,8,9 (9 digit) (any digit from these 9)

So, number of dighits does not contain 5 in between in between 10000 and 99999 (inclusive) = 8*9*9*9*9 = 52488