# Homework_1 - ENGG2430D Engineering Mathematics III Problem...

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ENGG2430D: Engineering Mathematics III Problem Set 1: Spring 2014 Due: Jan. 22, 2014 Reminder : Each student is supposed to turn in a separate solution in their own handwrit- ing. Please put down your own name and student ID in your submitted solution. Notice that all bold math notations are scalars in this problem set. Recap: Permutation : A permutation of a set of distinct objects is an ordered arrangement of these objects. An ordered arrangement of r elements of a set is called an r -permutation. The number of r permutations of a set with n distinct elements is P ( n, r ) = n ! ( n - r )! . Combination : An k -combination of elements of a set is an unordered selection of k ele- ments from the set. A combination is simply a subset of cardinality k . The number of k - combinations of a set with cardinality n with 0 k n is C ( n, k ) = n k = n ! ( n - k )! k ! . Binomial Theorem : Let x , y be variables and let n be a nonnegative integer. Then ( x + y ) n = n X j =0 n j x n - j y j .

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