Among $60$ apples collected from an apple tree, there are three bad apples. The apples are randomly placed into four baskets so that each basket contains $15$ apples.
(i)Compute the probability that the three bad apples are not all in the same basket.
(ii) Compute the probability that no two bad apples are in the same basket.
(iii) A farmer comes and chooses a basket at random. Compute the probability that there is exactly one bad apple in the basket that the farmer chooses.
(iv) Compute the expected number of baskets that contain exactly one bad apple.
I believe for (i), I could work out the total number of permutations of $3$ apples all in the same basket (maybe $60 \cdot 14 \cdot 13$) and divide by permutations of $3$ apples in $60$ positions ($60 \cdot 59 \cdot 58$).
For (ii), I know that there would be one empty basket, so there would be ($4C1$) ways of picking the basket of all good apples, but unsure of what to do from there.