Suppose that you have n coins that you flip simultaneously. How many ways are there to get k heads out of these n coins? I'll have you do this problem a couple different ways to illustrate a recursive and dynamic programming way of thinking, as well as the traditional mathematical way. Part A: Using the combinatorics that you learned in Discrete Structures/Discrete Math, what is the number of ways to get k heads out of n coin flips? Solution: Part B: Define the function numHeads (n,k) to be the number of ways you can get k heads from flipping n coins. Write a recurrence that expresses the number of ways to get k heads in n flips as a function of the number of heads that have turned up in n1flips1 Solution: Part C: Develop your recurrence into pseudocode. Since this is pseudocode, it doesn't need to be syntactically correct Java or any other language, but it should be easily human-readable. Solution: Part D: If you chose to do dynamic programming to speed up recursive code, would you do topdown or bottom-up dynamic programming? Why? Solution