MATH 2030 Quiz: MATH 2030 University of Manitoba Quiz 2

• School: University of Manitoba
• Department: Mathematics
• Course: MATH 2030
• Professor: All

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Instructor: r. craigen: time: 20 minutes no aids permitted, total marks: 20. Note: if an answer is 100 give this number; if larger, only obvious simpli cations are required. Answer: permutations of eeellxcnt permutations of letters e,l,x,c,n,t with multiplicities 3,2,1,1,1,1. Since 3 + 2 + 1 + 1 + 1 + 1 = 9 the answer is given by multinomial coe cient (cid:18) = 2 5 6 7 8 9 = 30240 (any of the last 5 expressions is worth full marks) [5: find all partitions of 4 into any number of parts. [5: in the lexicographic order, which permutation of the set {1, 2, . [5: explain why s(n, 2) = 2n 1 1. (clearly indicate if your answer is continued on the back of this sheet!) Answer: s(n, 2) enumerates the way of distributing n marked balls into 2 bins, leaving neither empty.