How many numbers between 1000 and 10,000 can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9? How many of them are odd?
Solution
There are the numbers between 1000 and 10000 would start with 1, 2, 3, 4, 5, 6, 7, 8, 9 and will have 4 digits. So that 4 digits filled from the 9 digits are arranged as
For the odd numbers only digits 1, 3, 5, 7, 9 can possible for the last digit. When fixed 1 as a last digit then remaining 3 digits filled by remaining 8 digits. So arrangement will be
Similarly for the last digits 3, 5, 7, 9, we get the arrangement ways 336 each time.
So that the total odd numbers arrangements are 336×5=1680
∴ The total numbers between 1000 and 10000 are 3024 and odd numbers are 1680