Student Name and ID Number
MATH 3012 Final Exam, December 8, 2003, WTT
1. Consider the following seven letter alphabet: {A, B , C, D, E, F , G}.
a. How many strings of length 19 have exactly 6 B’s?
b. How many strings of length 19 contain exactly 4 A’s, 2 B’s, 7 D’s and 6 G’s (and no C’s, E’s
or F’s)?
c. Of the strings described in part b, how many have all 4 A’s before the 7 D’s?
d. Of the strings described in part c, how many have the 4 A’s and the 7 D’s occuring together
as a block of 11 consecutive characters?
2. How many integer value solutions to the following equations and inequalities:
a. x1+x2+x3= 59, all xi>0.
b. x1+x2+x3<59, all xi>0.
c. x1+x2+x3= 59, all xi≥0.
d. x1+x2+x3≤59, all xi≥0.
e. x1+x2+x3= 59, all xi>0, x3>12.
3. In three space, consider moves from one point with integer coordinates to another formed by
adding one of (1,0,0), (0,1,0) and (0,0,1). How many paths from (0,0,0) to (8,5,9) can formed
with such moves?
