Here is an exercise I could not solve:
A = Number of 4-digit numbers, which do not have two equal consecutive digits.
B = Number of 4-digit numbers, which do not have two equal digits.
How much is A - B?
I translated the exercise, so it may sound a litter weird to you. Here is what I have done:
If I understood the condition for B correctly, only the 4-digit numbers that do not have repeated digits satisfy the condition, so $B = 9\times9\times8\times7$.
A includes B but also numbers that do have repeated numbers, just not one next to the other, something like $abca$ $abac$ $baca$, so $A = B + 9\times9\times8\times3$.
Which would mean $A-B = 9\times9\times8\times3$, which is incorrect because does not correspond to any of the four options for the answer.
I apologize in advance for any dumb errors. I have always done terribly at combinatorics.