Use Burnside's theorem to solve the following problems. (You receive little credit if you use other methods.) a) Determine the number of circular permutations of a multiset S = {R, R, R, B, B, B}. (b) Determine the number of different necklaces that are made up of three red beads and three blue beads. a) Prove that (2, 4, 5, 6, 10} is a difference set in Z11 and find all parameters of the SBIBD developed from this set. (You do not need to show this SBIBD.) b) Is there a Steiner triple system with V=3q+2 for some integer q and A=2? Explain your answer. Paragraph V BI U A + (a) (12 points) Solve the recurrence relation hn (n 2) with initial values ho = 1, h1 5hn-1+6hn-2 = 2. (b) (8 points) Use the Euclidean Algorithm to find the multiplicative inverse of 15 in Z41. Paragraph > BI UA E + V 1 2 3 4 5 Let f = and C = (R, B, B, R, W) 45213 Find a) f*c. b) f-1 c) cycle factorization of f, and d) cycle factorization of f 11 11