# How many ways to represent a 3 binary digit number that starts with 1 XOR ends with 0?

Borrowing from this question. How many ways are there to represent a 3 binary digit number that starts with 1 XOR ends with 0? I calculated the following:

• number of ways to start with 1xx :$$2^2$$
• number of ways to end with xx0: $$2^2$$
• number of ways for both 1x0 : $$2^1$$

Mathematically I got the answer as $$2^2 +2^2-2^1 = 6$$ but using a tree diagram I found only 4 possible combinations: that is 101 111 000 010

I would like some help to pinpoint where I went wrong.