Sometimes these things have sort of a strange feel to them. I will speak on something very similar to question b): the set of all ordered n-tuples of real numbers in [0,1). Suppose our n-tuples have the form
$$ ( 0. \gamma^1 _1 \gamma^1 _2 \gamma^1 _3 \gamma^1 _4 ..., 0. \gamma^2 _1 \gamma^2 _2 \gamma^2 _3 ..., 0. \gamma^3 _1 \gamma^3 _2 ..., ..., 0.\gamma^n _1 \gamma^n _2...)$$
Then we can associate a distinct real number to each ordered n-tuple by simply going through the 1st digits of all the numbers, then the second, then the third, and so on. i.e. we associate the number $$0. \gamma^1_1 \gamma^2_1 ... \gamma^n_1 \gamma^1_2 \gamma^2_2 ... \gamma^n_2 \gamma^1_3 ...$$ and so on. If we require numbers to be written in non-terminating decimals only, then this satisfies the required relationship.
In addition, we know that there is a bijection between all real numbers and the reals in $[0,1]$, so this is a bit closer to directly answering your homework question than I might have liked to admit. But this is an example of the sort of flavour of these questions.