Determine the number of 6-digit numbers that do not have the consequence 17th For example 4713.1572 allowed 5-digit numbers but 1723,3175,0254 are not allowed.
Consider one digit at a time. If you get a 1 then you have to make sure the next number is not a 7. So if you have 6 digits then you need to check each digit individually with six layers of branches.
First digit is > 1 then go to the next digit. If 1 you can only have 8 possibilities for the next digit instead of 9. You will also have to decide whether you can start with a 0 or not.
Each branch has two choices to consider: you either got a 1 before and need to check for a 7 or you didn't get a 1 and just pick any number. There are 2^5 choices or 32 choices to consider as a tree diagram but you can derive a formula to calculate this (leave the first out because you can always choose a number for first digit).
You should probably show us what you have tried, but if you use a tree diagram you will get 32 different combinations and then you add up the ones where you don't get a 17 in them (you will add up 16 different set of combinations to get the answer).
What I will ask you to do is to outline what you are covering in class: I think this is going to be easier than if I make an attempt on my own since it might be even more confusing.
The tree-approach method above is the best general way to go from a visual tree to a numerical answer (for both combinations of things and probabilities), but you are either not getting it or can't make use of it for reasons I don't know.