Permutations\Combinations from digits

Question

Using digits 1,2,3,4,5,7 only, how many numbers could be made that are between 2500 and 5000, if a digit is not repeated?

^{(If it had been 2000-5000, that would have been easy!!!)}

The answer at my level should only use $^nP_{r}$, $^nC_{r}$ and\or factorial notation.

Answer 1

HINT: how many are between 3000 and 5000 (inclusive)? For 2500 and 3000, you are really asking how many are between 500 and 999 (inclusive), not using the digit 2 either.

Answer 2

Since you say 2000 to 5000 is easy, all you have to do is do that and then subtract the ones between 2000 and 2500. And how many of those are there? Well, how many choices for the first digit? for the second digit? the third? the fourth? and what do you do with those numbers?