MATH 3013 – Discrete Mathematics
Directions:
Show the significant steps of your work clearly for ALL problems. You may receive zero or reduced points for insufficient work.
- Find an explicit formula for the recurrence relation
- (a) an = −3an−1 + 11an−2 + 3an−3 + 10an−4
- (b) an = 13an−1 − 57an−2 + 99an−3 − 54an−4
- Solve the recurrence relation subject to the initial conditions
- (a) wn = −10wn−1−25wn−2, and w0 = 5, w1 = −30
- (b) −3sn = 4sn−1 − 4sn−2, and s0 = −1, s1 = 2
- Assume that (4 − t2)Σ∞ n=2n(n − 1)antn−2 = −2Σ∞ n=0antn for all t.
- (a) Show that the coefficients an is given by the recurrence relation an+2 = −(n − 2)an 4(n + 2) , for n ≥ 0.
- (b) If a0 = −2, a1 = 6, find a2, a3, and a4
- The options available on a particular model of a car are four interior colors, seven exterior colors, three types of seats, five types of engines, and two types of radios. How many different possibilities are available to the customer?
- How many different car licensed plates can be constructed if the licenses contain four letters followed by three digits if
- (a) repetitions are allowed?
- (b) repetitions are not allowed?
- How many strings can be formed by ordering the letters ”SUBBOOKKEEPER”.
- Two dice are rolled simultaneously. How many out- comes give a sum
- (a) of 2?
- (b) less than 9?
- (c) greater than or equal to 5?
- In how many ways can we select a committee of three men and five women from a group of seven distinct men and nine distinct women.?
