Homework question and while there are very similar questions already answered my real concern is what the denominator should be in this question $8!$ or $4!$ since it is asking for the probability and not the number of possible arrangements.
The way I read it there are 8! possible ways to randomly order the boys and girls and then in the numerator there should only be two ways to alternate boys and girls??
so my answer is $2/8!$ but I'm unsure if this is correct??
Best Answer
Alternatively, there are $\binom{8}{4}$ ways to chose the positions of the girls, and only $2$ ways of picking the locations so that they alternate with the boys, for a probability of $$\frac{2}{\binom{8}4}$$