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198
( )
P(C
I
D)
=
P(C)P(D
I
C)
=
.2(.4)
=
114
.
()
e
P(D).7
.
,usmg
c.
Solutions to Exercises
Exercises 7.5
1. [BB] Think of the dolls as identically colored marbles and the shelves as boxes.
The answer is
(30~~
1)
=
(~g).
2. (a) 5
15
(b) There are
C8
5
)
ways to select the questions to be answered correctly. Now the other seven ques
tions must be answered incorrectly; there are 47 ways in which this can be done since there are
four wrong answers to each question. The answer is
C8
5
)
4
7
.
3. [BB] Each outcome can be signaled by dropping five identical marbles into six boxes labeled 16. The
answer is
(6+~1)
=
C50)
=
252.
4. [BB]
C01~1)
=
G~)
=
286
5. (a) Each bunch is specified by dropping six marbles into five boxes, each labeled with the color of a
rose. The answer is
(5+~1)
=
C60)
=
210.
(b) There is only one additional rose to be selected after the mandatory five different colored roses are
selected. There are only five possible bunches.
6. (a) [BB] The varieties are boxes. A selection can be indicated by dropping marbles into boxes. There
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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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