Question

How many 4-digit positive numbers less than 4670 that can be formed using the digits 1, 3, 4, 5, 8, 9 if repetition is not allowed. 

Answer 1

We need to group numbers.

Start with numbers beginning with 1. We have 5 digits left and there are 60 permutations of 3 digits out of 5, so there are 60 numbers starting with 1.

The same applies to 3: 60 numbers. So far we found 120 4-digit numbers.

Now starting with 41. We have 2 more digits to pick out of 4. There are 12 permutations, so there are 12 numbers starting with 41.

The same applies to numbers starting with 43 and 45. So we have 36 numbers to be added to 120=156.

There are 156 4-digit numbers below 4670 made up of the given digits.