[Math] How many numbers between 4,000 and 7,000 can be chosen using the digits [0, 8]

combinatorics

I have a homework problem in combinatorics, and I am struggling to solve it because I didn't understand our lesson well.

Can you please help me to solve this problem?

How many numbers between 4,000 and 7,000 can be chosen using the digits 0, 1, 2, 3, 4, 5, 6, 7, and 8 if each digit must not be repeated in any numbers?

PS: I don't have the resources to solve this. I just don't understand what our professor taught us, but we have already made a make-up class to solve this conflict.

Best Answer

HINT...you have a choice of 4, 5 or 6 for the first place (from left to right).

You then have a choice of 8 digits for the second place (including 0 but excluding your first choice).

Then you have a choice of 7 digits for the third place..... can you finish this?