In this problem we want to calculate the number of two-element lists .a; b/ we can form
Chapter 13, Problem 13.6(choose chapter or problem)
In this problem we want to calculate the number of two-element lists .a; b/ we can form using the numbers 0, 1, . . . , n with a < b. a. Show that the answer is .n C 1/n=2 by considering the number of two-element lists .a; b/ in which a < b or a > b. b. Show that the answer is also 1 C 2 C C n.Taken together, (a) and (b) prove the formulaXnkD1k D.n C 1/n2:
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