Part 1 of 2
How many ways can a student pick five questions from an exam containing eleven questions?
There are 462 ways to pick five questions from an exam containing eleven questions.
Part: $1 / 2$
Part 2 of 2
How many ways are there if he is required to answer the first question and the last question?
There are 1 ways if he is required to answer the first question and the last question.

Step 1 ：The first part of the question is asking for the number of combinations of 5 questions that can be chosen from 11. This is a standard combination problem, which can be solved using the combination formula: \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Step 2 ：Using the combination formula with n=11 and k=5, we find that there are \(\boxed{462}\) ways to pick five questions from an exam containing eleven questions.

Step 3 ：For the second part of the question, since the student is required to answer the first and last question, we are essentially choosing 3 questions from the remaining 9 (11 total questions - 2 required questions). So we can use the same combination formula, but with n=9 and k=3.

Step 4 ：Using the combination formula with n=9 and k=3, we find that there are \(\boxed{84}\) ways to pick three questions from the remaining nine questions after the student is required to answer the first and last question.