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question a derive a formula for the number of permutations of n objects of k different types where there are n1
question a let n and r be positive integers explain why the number of solutions of the equation x1 x2
question a explain how to find a formula for the number of ways to select r objects from n objects when repetition is
question a state the binomial theoremb explain how to prove the binomial theorem using a combinatorial argumentc find
question what is meant by a combinatorial proof of an identity how is such a proof different from an algebraic
question a what is pascals triangleb how can a row of pascals triangle be produced from the one above
question a what is the difference between an r-combination and an r-permutation of a set with n elementsb derive an
question a state the pigeonhole principleb explain how the pigeonhole principle can be used to show that among any 11
question how can you find the number of possible outcomes of a playoff between two teams where the first team that wins
question suppose that the name of a file in a computer directory consists of three digits followed by two lowercase
question list all 3-permutations of 1 2 3 4 5 the remaining exercises in this section develop another algorithm for
question a how can the product rule be used to find the number of functions from a set with m elements to a set with n
question how many ways are there to distribute five balls into three boxes if each box must have at least one ball in
question suppose that a basketball league has 32 teams split into two conferences of 16 teams each each conference is
question suppose that a weapons inspector must inspect each of five different sites twice visiting one site per day the
question how many ways are there to travel in xyz space from the origin 0 0 0 to the point 4 3 5 by taking steps one
question a professor packs her collection of 40 issues of a mathematics journal in four boxes with 10 issues per box
question a student has three mangos two papayas and two kiwi fruits if the student eats one piece of fruit each day and
question how many different bit strings can be transmitted if the string must begin with a 1 bit must include three
question there are 10 questions on a discrete mathematics final exam how many ways are there to assign scores to the
question suppose that a large family has 14 children including two sets of identical triplets three sets of identical
question a book publisher has 3000 copies of a discrete mathematics book how many ways are there to store these books
question a croissant shop has plain croissants cherry croissants chocolate croissants almond croissants apple
question show that a nonempty set has the same number of subsets with an odd number of elements as it does subsets with
question this procedure is used to break ties in games in the championship round of theworld cup soccer tournament each