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DISCRETE STRUCTURES - CMSC 203 - EXAM 3 - Fall 1996
1. A restaurant’s menu consists of 8 beverages, 11 appetizers, 6 salads, 24 entrees, 9 desserts, and
12 aperitifs. How many distinct dinners can they serve if each dinner contains:
(a) a beverage, an appetizer, a salad, an entree, a dessert, and an aperitif?
(b) a beverage, either an appetizer or a salad, an entree, and either a dessert or an aperitif?
2. How many ways can I arrange 6 Comedy video tapes, 7 Action tapes, 8 Drama tapes, 9 Horror
tapes, and 10 Foreign tapes on a shelf if:
(a) I want all the Action tapes first, followed by the Comedy tapes, then the Drama tapes, then the
Foreign tapes, and finally, the Horror tapes last?
(b) I only want all the tapes of the same type to be grouped together?
3. How many permutations are there of the words: (a) COMPUTER
(b) CALCULATOR
4. (a) How many CRAY words are there ? (A CRAY word contains eight 8-bit bytes)
(b) How many CRAY words contain no repeated bytes?
5. How many integer solutions are there to: A + B + C + D + E + F = 60
( a) with A, B, C, D, E, F > 0? (b) with A > 2 B > 1 C > 5 D > 0 E > 4 and F > 7?
6. Show that
7. Use the Iteration Method to solve the Recurrence Relation, sn+1 = 7sn − 2 with s0 = 1.
8. (a) How many initial conditions are needed to find the particular solution of the recurrence
relation, sn = 3sn−1 − 5sn−2 + 8sn−4 + sn−5 + 28sn−6 − 5sn−18 ?
(b) Find the general solution of : sn = 45sn−2 − 4sn−1 .
(c) Find the particular solution of the recurrence relation whose general solution is:
sn = D(7)n + E(9)n, when s0 = −1 and s1 = −15 ?
n
k
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⎛⎞ n
k1+
⎝⎠
⎛⎞
+n1+
k1+
⎝⎠
⎛⎞
=
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