A king has n children, at least one of them is a daughter. What’s the probability that all of them are daughters? A king has n children, at least one of them is a daughter. What’s the probability that all of them are daughters?

So far I've considered the case of 3 children, which gives a probability of 1/7.
But I'm confused about how to generalise this?
The sample space has $2^n$ equi-probable points, assuming P(boy) = P(girl) = $\frac12$

Knowledge that there is at least one girl implies that one particular outcome is ruled out.

Continue....
Its generalisation can be P(n,1)+P(n,2)+....+P(n,n) where p represents permutation abd their addition is no of ways of having children.
So probability is P(n,n)/total no of ways of having children which is the above sequence