Problem 13: Permutation

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