Order doesn't matter in the sense that the observed data set is unordered (just counts of girls and boys). What matters is how many ways there are that the universe can give rise to those unordered data sets. And in fact, there are more ways that the universe can give rise to the unordered state 1 boy 1 girl, than to the unordered state 2 boys. For similar reasons , there are more ways in which your papers can be in a mess across your desk than ways in which your papers can be neatly piled up.
And to count how many ways the universe can give rise to the unordered data sets, the usual technique is to expand the unordered data sets into all the equivalent ordered data sets, and count the latter.
And to count how many ways the universe can give rise to the unordered data sets, the usual technique is to expand the unordered data sets into all the equivalent ordered data sets, and count the latter.