# Discrete and Combinatorial Mathematics

May 12th, 2015
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* 5. Consider the following program segment (written in pseudocode): for i := 1 to 123 do for j := 1 to i do print i * j a) How many times is the print statement of the third line

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MTH 221 Week 2* Ch. 4 of Discrete and Combinatorial Mathematics* * Exercise 4.1, problem 5a* 5. Consider the following program segment (written in pseudocode):for i := 1 to 123 dofor j := 1 to i doprint i * ja) How many times is the print statement of the third line* executed? (n)(n+1)/2 * n = 123. The answer should be 7626* * Exercise 4.2, problem 18a Consider the permutations of 1, 2, 3, 4. The permutation 1432, for instance, is said to have one ascentnamely, 14 (since 1 < 4). This same permutation also has two descents namely, 43 (since 4 > 3) and 32 (since 3 > 2). The permutation 1423, on the other hand, has two ascents, at 14 and 23and the one descent 42. a) How many permutations of 1, 2, 3 have k ascents, for k _ 0, 1, 2?Premutations of (1,2,3) have 1 zero ascent, 4 ascents of 1 and 1 ascent of 2 * * Ch. 4 of Discrete and Combinatorial Mathematics* *

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