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190
Solutions to Exercises
5.
[BB]
(a)
(b)
(~)
_
15.
M 
64'
(c)
1
+
(~)
+
(~)
_
11.
64

32'
6.
(a)
(d)
(d)
1
1 _
63.
6464'
1
+
G)
1
~=16
(b)
(e)
(~)
+
(~)
+
(~)

1
64

2'
(e)
G)=~
128
128
(i)+G)+G)+G)
_1
128

2"
(c)
1
1
+
(i)
_
15.
~16'
7.
[BB]
(a) There are
(~)
outcomes
in
the sample space. For an outcome to be in the event described, we
need to choose three from the six selected numbers and three from the 43 other numbers. The answer
l
'S
m
(~) ~
0 018
(~)
~.
.
1
(c)
1 
(~) ~
1.000.
9. [BB] (a)
1~~~~)
=
i;
(b)
1
i
=~;
(c)
1
l~f~~) =~;
(d)
;1W~?
=
1
5
8;
(e) We will use the formula given
in
part (3) of Theorem 7.3.2. Let
A
be the event "at least one white
ball" and
B
be "exactly one red ball." We saw in (c) that
P(A)
=
~.
Also
P(B)
= ;Wg? =
~~.
Since
An B
is the event described in (d),
P(A
n
B)
=
1
5
8' The required probability is
P{A
U
B)
=
5
35
5
55
9"
+
72 
18
=
72'
10
()
3(3)
_
1 .
.
a 12(12)
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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