Question

I'm a bit stuck on this question:
Caleb needs to create an 8-digit password using only numbers. How many different passwords are there if he wants to use 00 exactly once?​

There's no answer choices, I'm supposed to show all my work. Please help!

Answer 1

this problem is discussed many time.
Try google.

Answer 2

Start by placing the 0 0 side by side...
_ _ _ _ _ _ _ _ so the 0 0 could go
0 0
0 0
0 0
0 0
0 0
0 0
0 0
So the 0 0 could be in 7 places. So place them first (they could fill any of 7 spots... so they are 7)
7 _ _ _ _ _ _ which means there are 6 other spots to fill
now the other spots could each have the numbers 1-9, that is 10 numbers...
7 x 10 _ _ _ _ _ but then the condition says that the numbers have to be different ... so once you have used a digit it is no longer available. So in the next spot there are only 9 choices etc
7 x 10 x 9...
I hope this is enough of a hint to get you started : )

Answer 3

Oh drat! The program didn't show the 0 0 being shifted over to the next two spots in each of the lines beneath the first one.
0 0 _ _ _ _ _ _
_ 0 0 _ _ _ _ _
_ _ 0 0 _ _ _ _
_ _ _ 0 0 _ _ _
etc...