, , and .
How many people are in at least one of the sets?
Q10. A student wishes to take
an English Course (offered at 8, 10, 11 and 12),
a Math Course (offered at 9, 10, 12 and 1) and
a Comp Sci Course (offered at 9, 11, 12 and 1)
How many different schedules are possible so that they make take all three courses?
Q11. You are in a grocery store to purchase 10 pizzas, there are 5 varieties to choose from, in how many different ways you can purchase 10 pizzas providing a repetition is allowed?
Q12. Consider the equation W + X + Y + Z = 20, how many different solutions providing , we are only concerned with positive integers W, X, Y and Z.
Q13. Let S be a finite set containing 12 elements, which we wish to partition into Cells C1, C2, C3, and C4, such that n(C1) = 2, n(c2) = 2, n(C3) = 3, n(C4) = 5.
How many such partitions are possible?
Q14. List cycles’ sizes for the following permutation:
![alpha equals open parentheses table row a b c d e f g h row c e b d a g h f end table close parentheses]()
Q15. Suppose that you are looking at permutations of {1, 2, 3, 4, 5, 6, 7, 8}.
How many permutations are there with the cycle structure (a, b, c, d) (e, f, g, h)?
(
)
10,6
C
(
)
5,2
P
(
)
11,8
P
A
B
C
(
)
85
nA
=
(
)
40
nB
=
(
)
50
nC
=
(
)
9
nAB
Ç=
(
)
12
nAC
Ç=
(
)
7
nBC
Ç=
(
)
2
nABC
ÇÇ=
(
)
5,2
C
ABRAHAMLINCOLN
HW-5-Counting_Techniques1.docx
0
