No, that's about all you can do.
Just your luck it was only for 4 children, which means there would be 2^4 or 16 cases.
Just go about it systematically.
Just imagine if there had been 6 kids.
An experiment consists of recording in order of their births, the sex composition of a four child family in which the children were born at different times.
Describe an appropriate sample space s for this experiments
I can do
GGGB, BBBG,GBGB,BGBG,BBGG,GGBB,BGGG,GBBB..... but is there a less tedious method to do this?
2 answers
birthday 1, 2 choices
birthday 2, 2 choices
birthday 3 , 2 choices
birthday 4, 2 choices
2*2*2*2 = 2^4 = 16
b b b b
b b b g
b b g b
b b g g
---------
b g b b
b g b g
b g g b
b g g g
----------------
g g g g
g g g b
g g b g
etc
birthday 2, 2 choices
birthday 3 , 2 choices
birthday 4, 2 choices
2*2*2*2 = 2^4 = 16
b b b b
b b b g
b b g b
b b g g
---------
b g b b
b g b g
b g g b
b g g g
----------------
g g g g
g g g b
g g b g
etc