What are the chances of rain on particular days I study maths as a hobby and am on to elementary theory of probability.
I have come across this problem:
Find the probability of events A, B and C given it rained on exactly 2 days last week.
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*The key observation here, as you have mentioned, is the number of total outcomes, which is $\begin{pmatrix}7\\2\end{pmatrix}=21$. Equipped with this fact, you can proceed by finding out what is the number of outcomes that fulfills each part.

*Yes, the first part is just $\frac{1}{21}$, taking one of the 21 possible combinations.

*On the second part, notice that there are just 6 out of 21 possible outcomes that makes the raining days consecutive (day 1 and 2, 2 and 3, ..., 6 and 7). Therefore, the possibility is just $\frac{6}{21}=\frac{2}{7}$.

*As for the third part, you would want to see how many combinations in them are not on two specific days. That would mean those combinations are only chosen from the other five days. So that would be $\begin{pmatrix}5\\2\end{pmatrix}=10$. Therefore there are 10 out of 21 possibilities that fulfill the requirement. The probability is $\frac{10}{21}$.

