You have decided to divide a deck of cards into two piles; one of 22 cards, and

Question:

You have decided to divide a deck of cards into two piles; one of 22 cards, and one of 30.

(a) You pick the 30 cards for pile 1, and the remaining 22 are put into pile 2. How many divisions into 2 such piles are possible?

(b) You decide to instead pick 22 cards for pile 1, and let the remaining 30 be put into pile 2. How many divisions into two such piles is possible?

(c) Why are these two answers the same?

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