Stuck again on disributions

I have another question. Again I'm in a college probability class studying multivarate distributions.

Here goes:

In a clinical study of a new drug formulated to reduce the effects of arthritis, researchers found that the proportion p of patients who respond favourably to the drug is a random variable that varies from batch to batch of the drug. Assume that p has a probability density function given by

f(p)={12*(p^(2))*(1-p), whenever p is between 0 and 1 inclusive

{0, whenever p is elsewhere.

Suppose that n patients are injected with portions of the drug taken from the same batch. Let Y denote the number showing a favourable response.

(A) Find the unconditional probability distribution of Y for general n.

(B) Find E(Y) for n = 2.

I'm confused because there's no Y1 and Y2. I would love any help.