MAE 3020
Assignment 1 solutions
1. S1 = {MMMM, MMMF, MMFM, MFMM, FMMM, MMFF, MFMF, MFFM,
FMFM, FFMM,FMMF, MFFF, FMFF, FFMF, FFFM, FFFF};
S2 = {0, 1, 2, 3, 4}.
A  C = {0, 2, 3, 4, 5, 6, 8}
AB=
C’ = {0, 1, 6, 7, 8, 9}
(C’  D) = {1, 6, 7}
(C’  D)  B = {1, 3, 5, 6, 7, 9}
(e) (S  C)’ = C’ = {0, 1, 6, 7, 8, 9}
(f) A  C = {2, 4}
D’ = {0,2,3,4,5,8,9}
A  C  D’ = {2, 4}
2. (a)
(b)
(c)
(d)
3. By multiplication rule, the number of ways = 8*3 = 24
4. (a) With n1 = 4 possible answers for the first question, n2 = 4 possible answers for
the second question, and so forth, the generalised multiplication rule yields
4*4*4*4*4 = 1024 ways to answer the test.
(b) With n1 = 3 wrong answers for the first question, n2 = 3 wrong answers for the
second question, and so forth, the generalised multiplication rule yields
3*3*3*3*3 = 243 ways to answer the test and get all questions wrong.
5. (a) 6! = 720
(b) A certain 3 persons can follow each other in a line of 6 people in a specified
order in 4 ways or (4)(3!) = 24 ways without regard to order. The other 3 persons
can then be placed in line in 3! = 6 ways. Hence, there are (24)(6) = 144 ways to
line up 6 people with a certain 3 following each other.
(c) A certain 2 persons can be placed in line without regard to order in (5)(2!) = 10
ways. The other 4 persons can then be placed in line in 4! =24 ways. Then, there
are 10*24 = 240 ways to line up 6 people with certain 2 together. From (a), there
are then 720 – 240 = 480 ways if a certain 2 refuse to follow each other.
-7 5-3
6. The number of ways is: C712C12
3 C2 
12!
 7920
7!  3!  2!
7. The number of ways is:
9!
9!
9!
9!
9!




 4410
1!  4!  4! 2!  4!  3! 1!  3!  5! 2!  3!  4! 2!  2!  5!
8. Define
M: industry will locate in Munich
B: industry will locate in Brussels
(a) P(M  B) = P(B) + P(M) – P(B  M) = 0.7 + 0.4 – 0.8 = 0.3
(b) P(M’  B’) = 1 - P(M  B) = 1 – 0.8 = 0.2
9. There are N= 26*25*24*9*8*7*6 = 47,174,400 possible ways to code the items
of which n = 5*25*24*8*7*6*4 = 4,032,000 begin with a vowel and end with an
even digit. Therefore, n / N = 10 / 117.
1 8 
  
1 2
1
10. (a) The probabilit y     
3
9
 
 3
 5  3 
  
2 1
5
(b) The probabilit y    
14
9
 
 3