How to describe this structure in spoken words?

If this is at a beginning level:

$f$ of zero equals the probability that $X$ equals $0$; this is a fraction whose numerator is $3$ choose $0$ times $17$ choose $2$, and whose denominator is $20$ choose $2$. This evaluates to the fraction $68$ over $95$.

If the students are a bit more advanced, you can compress it a bit:

$f$ of zero equals the probability that $X$ equals $0$, which is $3$ choose $0$ times $17$ choose $2$ all over $20$ choose $2$, which simplifies to $68$ over $95$.

There are so many different ways that you can do this. Fractions can be read as "[something] divided by [something else]", "numerator: [something] denominator: [something else]" or variations thereupon. Each version has its benefits, so I recommend experimenting with it. As for parenthesis, reading them out loud is not always necessary. In your example, you can get away with not reading them. Nonetheless, I think pauses after each function is helpful to the listener. Here is my recommendation:

"$f$ of $0$ [pause] equals the probability that $X$ equals $0$ [pause] equals $3$ chose $0$ [pause] times $17$ chose $2$ [pause] divided by $20$ chose $2$ [pause] equals $68$ $95^{\text{ths}}$"

I would read it as the probability that X equals zero, then three choose zero times seventeen choose two divided by twenty choose two.