How many 7-digit phone numbers are possible, assuming that the first digit can’t be a 0 or a 1 I use the multiplication rule. 
For the first digit I have 8 choices. For the last 6 digits I have 10 choices for each. So answer is $8 \cdot 10 ^6$.
Is there any other way to solve this problems. I usually gain a lot of insight from solving the problems in different ways. Please write which theorems etc. you have used. 

number of 7 digit numbers ( including leading 0):  10,000,000
number of 7 digit numbers including lead 0 or 1 :  - 2,000,000
number of 7 digit numbers not lead by 0 or 1 :          8,000,000
This more just taking a complement of a set. ( so an interior form of inclusion-exclusion)
You could realize all 7 have at least 8, get $8^7$ then realize each of 6 have 2 more with the seventh having $8=2^3$, for $2^9$ and have fun adding up all $64=2^6$ combinations all together. More a property of a powerset which relates to combinations, as the total number of combinations of all sizes, is the number of distinguishable states which in includes all subsets, (Also tedious) 
