Equally likely question help

Doing some past paper questions and need help with this question (screenshot). https://gyazo.com/2d0e8d0f5f40b38d768e005f5b47a8cb https://gyazo.com/4480cef1be6706344b59772c9e437d1a

I've got a as |S| 220 (12 choose 3).

For b I'm not sure how to do it although I have an idea. My guess would be |E| = 4 choose 3 x 6 choose 2, since there are 4 numbers less than 5 and 3 slots to choose and 6 odd numbers and 2 slots left. Then the P(E) = |E|/|S|. Is this at all correct?

For c and d I've no idea how to do it

An urn contains 12 balls, numbered 1 to 12....

For interested readers, the exercise at the remote location is as follows:

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An urn contains 12 balls, numbered 1 to 12. The balls in the urn are thoroughly mixed and three balls are selected at random in such a way that any subset of three balls is equally likely to be selected. The sample space of this experiment can be described as:

\(\displaystyle S\, =\, \left\{\, \{i,\, j,\, k\}\, :\, 1\, \leq\, i,\, j,\, k,\, l\, \leq\, 12\, \mbox{ and }\, i\, \neq\, j,\, j\, \neq\, k,\, i\, \neq\, \right\}\)

(a) Determine |S|, the size of the sample space S, and explain why it is reasonable to define P({i, j, k}) = 1/|S| for any subset, {i, j, k}, of three balls from the urn.

(b) Find the probability that at least one of the numbers on the three selected balls is less than 5 and at least one of the numbers is odd.

(c) Find the conditional probability that all the numbers on the selected balls are greater than 7 given all the numbers on the selected balls are even.

(d) Find the conditional probability that the three numbers on the selected balls are consecutive given all numbers on the selected balls are less than 5.

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The error in the set-statement is in the original. No work is shown at the remote location.