Proportion of amino acids from a random polymer of U and C
The first thing to mention is that this is the type of experiment that Marshall Nirenberg performed in order to break the genetic code, and for which he got the Nobel prize in 1968. We stand on the shoulders of giants.

If the ratio is U:C, 1:5, then it is easy to calculate the probability of encountering each of the 8 possible codons composed by just U and C. So for example:

the probability of UUU is (1/6)3

the probability of UUC is (1/6)2*(5/6)

and so on.

Here's a Table that gives all of the values and demonstrates that the answer is (D).