If a couple plans to have eight children, how many different gender sequences are possible

If you call a boy '0' and a girl '1', then the number of possible patterns
is exactly the highest binary number you can count to with 8 binary bits.

8 binary bits make one 'byte'.  It has 256 possible values.

If the couple does have 8 children ... (we wish them well, we hope
all the children are born strong and healthy, we hope their mother
stays healthy and strong enough to raise all of them, and we hope
their father stays strong and healthy enough to work and bring home
enough bagels and lox for all of them) ... then there are 256 possible
gender sequences ... boy-girl-girl-boy-boy- etc. 

There is no question, there is just the answer.

The first one is correct