Problem 4. Combinatorics (20 points) Note: in this problem, you do not have to multiply out factorials, or divide out fractions. However, if the top and bottom of a fraction have stuff that cancels out, please do that. a) Given a group of 17 different pictures, how many ways are there to line them up into a row? b) Now we have a group of 17 pictures, where five are identical and the others are all different. How many ways are there to line them up into a row? c) How many ways are there to draw 3 cards from a deck of 52 so that exactly one of them is a heart? Note: having the first one be a heart and having the third one be a heat are considered different ways. d) How many ways are there to make an (unordered) pile of 3 cards from a deck of 52 so that exactly one of them is a heart