#Conditional Probability
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That's incorrect. In (a) you need to use hypergeometric distribution. After all, the probability of picking a female puppy changes each time you take a puppy out.
why is it x 4?
No, that's incorrect. Let's use the general formula.
We have X ~ HG(N = 9, D = 5, n = 4). For a hypergeometric rand variable:
P(X = k) = C(D, k)C(N - D, n - k)/C(N, n)
So, in our case:
P(X = 3) = C(5, 3)C(4, 1)/C(9, 4)
Now you just need to calculate it.