4. Six women and eight men are on the faculty in the mathematics department at a school. How many ways are there to select a committee of four members of the 1. Solve the congruence: 2x = 5(mod 11) . 5 b. 6 . 7 d. 8 department if at least one woman must be on the committee? a. 4242 b. 126 2. Find f(4) if f is defined recursively by: f(0) = f(1) = 1 and f(n) = f(n-1) + f(n-2) for n > 1. . 931 d. 1131 . 5 b. 25 5. True of False? a, = 2 a solution to the recurrence . 33 d. 1214 relationa, = 2a, -a,, with initial conditions a, = 2 and . az = 2 a. True b. False 3. Find the sequence for the recursive formula: s, =-+9, So =-3 . 14, -4, 14, -4 b. 6, 14, 86, 734 . -3, 12, -3, 12 d. -3, 9, -3, 9 6. Find a solution to the recurrence relation: a, = 3na1a, = 2 a. a, = 3" - n! b. a, = 2.3" - n! C. a, = 2.3" -n d. a, =2-3" 7. A connected planar graph has 28 edges. If a planar representation of this graph divides the plane into 16 regions, how many vertices does the graph have? . 14 b. 12 . 10 d. None of the above 8. True or False? The following relation is an equivalence relation: {(0,1),(1,1),(2,1),(3,3)}. a. True b. False