Problem 2. (15 points) Our AMS 311 exam will test students on some of the 50 key facts about probability. Marc will randomly pick 10 of the 50 facts to put on the exam. Each student gets to pick 6 out of the 10 to state and explain. Bob (an AMS 311 student) is trying to decide how many facts he should study to prepare for the exam. Bob studies k of the facts (where k is an integer between 0 and 50). Let X be the number of AMS 311 facts appearing on the exam that Bob has studied. What is the distribution of X? (If it is a named distribution, give the name and the parameter(s), in terms of k, and some justification).