Write a program that takes the values of n and k as inputs and displays as output the value n choose k.

The phrase “n choose k” is used to refer to the number of ways in which we can choose k objects from a set of n objects, where n >= k >= 0. For example, “52 choose 13” expresses the number of possible hands that could be dealt in the game of bridge. Write a program that takes the values of n and k as inputs and displays as output the value n choose k. Your program should define a recursive function, nChooseK(n, k), that calculates and returns the result. When the program has finished interacting with the user, it should print a table of results that show how nChooseK increases with n and also how nChooseK increases with k. (Hint: We can partition the selections of k objects from n objects as the groups of k objects that come from n – 1 objects, and we can partition the groups of k objects that include the nth object in addition to the groups of k – 1 objects chosen from among n – 1 objects.) (Caution: Don’t start your testing with 52 choose 13, but with smaller numbers for k, such as 2, 3, 4, and so forth.)

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