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If
n
fair six
-
sided dice are tossed and the numbers showing on top are recorded, how many
(a)
record sequences are possible?
(b)
sequence contain exactly one six?
(c)
sequences contain exactly four twos, assuming
4
n
?
There are 4 adults and 6 children sitting around a round table. If there must be at least one child
between any two adults, then
how many ways are there for them to sit around the table? Rotations are
considered the same, while reflections are distinct.
(a)How many bit strings of length 8 contain at least 6 ones?
(b)How many bit strings of length 8 contain at least 3 ones and 3 zeros?
Show that
(
)
(
)
(
)
1,
,
1
,
CnkCnkCnk
+ =
− +
.
Prove that
(
)
(
)
1,
1
,
nPnnPnn
− − =
.
Show that if 𝑎𝑑−𝑏𝑐 ≠ 0, then the function 𝑓(𝑥)=𝑎𝑥+𝑏/𝑐𝑥+𝑑 is one-to-one and find its inverse.
Find the domain and range of the following function given by
𝑓(𝑥)=√(3𝑥−5)(𝑥+4)𝑥3−16𝑥.
Show that if 𝑎𝑑−𝑏𝑐 ≠ 0, then the function 𝑓(𝑥)=𝑎𝑥+𝑏𝑐𝑥+𝑑 is one-to-one and find its inverse.
Prove that for all integer n>=3, P(n+1,3) - P(n,3) = 3P(n,2)
.
cal expressions using predicates, quantifiers, and logical connectives. First, let the domain consist of the students in your class and second, let it consist of all people.
a) Everyoneinyourclasshasacellularphone.
b) Somebody in your class has seen a foreign movie.
c) There is a person in your class who cannot swim.
d) All students in your class can solve quadratic equa-
tions.
e) Some student in your class does not want to be rich
#339914 on Dec 2023