Problem 3 (15 pts]: Group Projects Suppose we had 18 students working on various projects each month. i. In January, there were 5 projects available. At least how many students are guaranteed to work on the same project? ii. In February, you learned at least 2 students worked on the same project. At most how many projects were available that month? iii. You overhear someone mention the following Remember when there were 516 students! They had 86 projects together and capped the number of students on a project at 6 students per project. Every project still had at least 4 students! Talk about crazy!\" Use what you have learned about the Pigeonhole Principle to explain why this scenario is possible.