How many bit strings of length six either begin with two 0s or end with three 0s?

This tells me that there are only two option available to begin with, 0 or 1.

For it to start with 2 0's, it would be 2^4=16

For it to end with 3 0's, it would be 2^3=8

Subtract 2^1 for the two instances that would have two 0's in the front and three 0's in the back.

So: 16+8-2=22

Is that correct?