A-1 = 1/1 * [1−21101−36001−40001]A-1 = [1−21101−36001−40001]2. How many ways can we rearrange the letters a b c d e f g h i j so that no vowel endsup in the position where it began?Solution: n=10 (a, b, c, d, e, f, g, h, i, j) Vowels a, e, i (3 vowels)No. of Ways= 2419143. Find a closed form for the generating function for each of these sequences.(a) 7, 3, 4, 6, 7, 3, 4, 6, 7, 3, 4, 6, . . .Solution: 1 mod 4 = 12 mod 4 = 23 mod 4 = 34 mod 4 = 05 mod 4 = 16 mod 4 = 27 mod 4 = 38 mod 4 = 0 And so on...F (n) = {ifnmod4=1,7ifnmod4=2,3ifnmod4=3,3ifnmod4=0,6} n E |N(b) .1, 0.01, 0.001, 0.0001, . . . Solution: a2/a1= a3/a2=...... an/an-1= 1/10a1= 1/10f(n) = an/an-1= 1/10; n≥2; n E |N; a1=1/10(c) 2, 5, 8, 11, 14, 17, 20, . . .
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