1. Counting (a) How many ways can x yellow balls and n-x red balls be put into n umns with one ball in each urn? (b) As above but now each ball is numbered and only yellow balls, no red. (c) n men sit around a round table that has 2n seats, leaving a seat between them. Women sit in these seats. If all people are distinguishable, how many arrangements of the people are there?

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Recurrence relation

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.