#1 How many total gifts are given just on day 10?

#2 How many total gifts are given during the twelve days?

#3 Suppose the song was changed to the “Nineteen Days of Christmas”? How many total gifts would my true love give to me?

#4 Generalize. How many gifts would be given on day n? How many total gifts would have been given on day n?

Here’s a discussion of the relationship of the song to Pascal’s triangle. The answers to #4 are C(n + 1, n – 1) and C(n + 2, 3). [Note: C(n+1, n-1) is translated as a “combination of n+1 things taken n-1 at a time”. Notation for combinations varies.] Can you prove that the two answers given will always work?

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