How many of these are less than 5000?

Question

In this version, you are to form a 4-digit number from the digits 1, 2, 3, 4, 7, 8, and 9, using each at most once.

 

How many of these are less than 5000?

Answer 1

The first number ≤ 4.

If 4, then ₆P₃ or 120

If 3, then ₆P₃ or 120

If 2, then ₆P₃ or 120

If 1, then ₆P₃ or 120

 

480 such numbers exist.