How many 4 digit numbers greater than or equal 3000 and less than 8000 can be formed with no repetition in their digits?

Question

How many 4 digit numbers greater than or equal to 3000 and less than 8000 can be formed with no repetition in their digits?

Answer 1

It's: 5 * 9 * 8 * 7

1. You can choose 5 numbers on the first place (3, 4, 5, 6, 7)
2. You can choose 10 - 1 (choosen in 1.) numbers -> 9
3. 9 - 2 (choosen in 1 and 2) -> 8
4. 9 - 3 (3 numbers on previous positions) -> 7

Answer 2

For all numbers between $3000$ and $3999$, you first choose the first leading "3" then it remains three "slots" which cannot be filled by a "3", this leaves you $\frac{9!}{6!}$ possibilities. (Since you have 9 numbers to choose without repetition and the order matters)

Same argument for $[4000,4999], ... , [7000,7999]$