The question is basic: If it's sunny an average of 5 days a week, what's the probability that it'll be rainy 2 days out of 3? Assume unrealistically that the weather on a given day is independent of the other days.
I'm having a major mental block and can't see through this problem. Does the binomial distribution apply; i.e.
$\dbinom{3}{2} \left(\frac{2}{7} \right)^2 \left(\frac{5}{7} \right)^1$
or is it a simple selection without replacement:
$\frac{\dbinom{2}{2}\dbinom{5}{1}}{\dbinom{7}{3}}$
I can't convince myself one way or the other; so I solicite your advice.