# Subtle Differences of Studying Permutations and Combinations Essay

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I understand you are taking a college course in mathematics and studying permutations and combinations. Permutations and Combinations date back through the ages. According to Thomas & Pirnot (2014), there is evidence of these mathematical concepts as early as AD 200. As we solve some problems you will see why understanding these concepts is important especially when dealing with large values. I also understand you are having problems understanding their subtle differences, corresponding formulas nPr and nCr and the fundamental counting principle. Before we review some exercises, I would like to provide you with some definitions you will need in solving some problems. According to Thomas & Pirnot (2014), a permutation is an ordering of…show more content…
616). Permutation Example: Eight books are placed on a shelf. How many ways are there to arrange the books? Solution: Suppose eight books are placed on shelf. The number of ways to do this in a straight line is P (8,8)=8x7x6x5…2x1=40,320. The number of permutations p (n, is the number of books to select from and r is the number of books we selected. We then arranged the books in order from high to low totaling 40,320 ways to arrange the books. If n is a counting number, the symbol n!, called n factorial, stands for the product n x(n-1)x(n-2)x(n-3)x…2x1. We define 0! = 1 (Thomas & Pirnot, (2014), p.624). Fundamental Counting Principle (FCP): Five Card Draw is a poker game in which each player is dealt an initial hand of five cards. How many unique five-card hands are possible? Note: There are 52 cards in a deck. Solution: In a five-card draw of a poker game, there are 2,598,960 hands possible. C(52,5)=52!/47!=52x51x50x49x48/5x4x3x2x1=2,598,960 ways possible. A deck of playing cards has 52 cards. You would read the solution as follows: The number of combinations in a 52 deck of cards (n) drawn at 5 (r) at a time is C(52,5). Using fundamental counting principle we determine 5 cards in a deck of 52 can be drawn 52 x 51 x 50 x 49 x 48 by 5, 4, 3, 2, 1 totaling 2,598,960 ways. Combination: To log into an IPad, a four-digit security code needs to be typed. The