A student must answer 5 out of 10 questions on a test, including at least 2 of the first 5 questions. How many subsets of 5 questions can be answered?
There are $\displaystyle \binom{10}{5}$ total five question subsets.
There is only one having none in the first five questions.
There are five having exactly one in the first five questions.
All the rest have at least two in the first five questions.