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186
Solutions to Exercises
(b) The answer is
9~4
=
462, one half the answer to (a) since, the unnamed teams {I, 2, 3, 4, 5, 6},
{7, 8, 9,10,11, 12} give rise to two possibilities for the Good Guys.
3. [BB] Choose the five positions for the l's and put the O's in the remaining places. The answer is
(
12)
12!
792
5
=
7!5!
=
.
4. This is the number of ways to select three locations from seven for the red flags. The answer is
G) =
3T~!
=
35.
6. [BB]
(~O)
+
CI0)
+
(;0)
+
C30)
=
1
+
10
+
45
+
120
=
176
7. (a) A game card can be completed in
(~)
=
13,983,816 ways.
(b) A player with one card has one chance in 13,983,816 of winning; a player with
n
cards has
n
chances in 13,983,816 . The smallest
n
such that
n/13,983,816
;::: 10
6
is
n
=
14.
(c)
==_:
__
:
___
;~=_=:_=__::=_:_
No numbers match
(~3)
=
6,096,454
Exactly one number matches
(~) (~3)
=
5,775,588
Exactly two numbers match
m
(~)
=
1,851,150
Exactly three numbers match
(~) (~3)
=
246,820
Exactly four numbers match
(~) (~3)
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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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