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By Alan Doerr, Kenneth Levasseur

Textbook from UMass Lowell, model 3.0

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Extra resources for Applied Discrete Structures

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If there are twentyfive players on the team, there are 25 · 24 · 23 · · · · · 3 · 2 · 1 different permutations of the players. This number of permutations is huge. In fact it is 15511210043330985984000000, but writing it like this isn’t all that instructive, while leaving it as a product as we originally had makes it easier to see where the number comes from. We just need to find a more compact way of writing these products. We now develop notation that will be useful for permutation problems. 5 (Factorial).

Order is important in permutations. Order is not important in combinations. 1 (Counting Permutations). How many different ways are there to permute three letters from the set A = {a, b, c, d}? 3)! 2 (Counting with No Order). How many ways can we select a set of three letters from A = {a, b, c, d}? 4. COMBINATIONS AND THE BINOMIAL THEOREM 37 order of the three letters. By trial and error, abc, abd, acd, and bcd are the only listings possible. To repeat, we were looking for all three-element subsets of the set A.

SUMMATION NOTATION AND GENERALIZATIONS 19 • The expression ak is the general term of the series. It defines the numbers that are being added together in the series. • The value of k below the summation symbol is the initial index and the value above the summation symbol is the terminal index. • It is understood that the series is a sum of the general terms where the index start with the initial index and increases by one up to and including the terminal index. 1 (Some finite series). 2 (More finite series ).

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