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Math 231 Homework #7 The problems on this homework are all to do with compositions. By def- inition, a composition of n, is a sequence (n.1, . . .,n.r) of positive integers summing to 11, i.e., n = 111 + - - - + or. The number 1' here is the number of ports in the composition. For example, here are the compositions of 5: (1,1,1,1,1); (1,1,1,2),(1,1,2,1), (1,2,1,1),(2,1,1,1); (1, 1,3), (1,3, 1), (3, 1, 1), (2,2, 1), (2, 1, 2), (1,2,2); (114},{411}1{2:3}1(312); (5)- 5. Let YR}, be the set of compositions of n which have r parts equal to 2 and all of the other parts are equal to 1. (a) Show that Y\