Calculating the probability that families of 4 children are composed of as many boys as girls.
Assuming here that each birth gives rise to a boy or girl with equiprobability.
The number of outcomes would be $2^4 = 16$
By manually calculating the number of outcomes where there are 2 boys and 2 girls we find $6$ arrangements.
Is there a general formula for calculating the number of arrangements where we have 2 boys and 2 girls?
Calculating the binomial coefficient solves the problem:
With $n ≥ k ≥ 0$
The general formula is: ${\displaystyle {\binom {n}{k}}={\frac {n!}{k!(n-k)!}}.}$
In this particular case:
${\displaystyle {\tbinom {4}{2}}={\tfrac {4!}{2!2!}}=6}$
Thanks to @EthanBolke for pointing to the binominal coefficient.