Section 7.5
199
9. (a) There are e50) ways for Philadelphia to select its players and then
C5
5
)
ways for Boston to
choose, then
C50)
ways for Miami, after which Toronto's players are detennined. The answer
is e50)
C5
5
)
C~)
=
5!;!~!!5!
=
11,732,745,024.
(b) Each answer to this question gives rise to 4! answers to part (a) since for each division into four
teams, there are 4! ways to assign them to four different cities. So the answer here is
5!5F5~k!4!
=
488,864,376.
10. There are
C6
2
)
ways in which San Diego can choose its players, then
(~)
ways for Houston to choose,
after which Toronto gets the remaining two players. By the multiplication rule, there are altogether
C6
2
)
m
=
924(15)
=
13860 possible drafts.
11. (a) [BB] Select the boxes for the red balls in one of
(~g)
ways, then the boxes for the white balls
in one of
(~g)
ways and finally the boxes for the blue balls in one of (ig) ways. The answer is
(
60) (50) (40)
60!
10
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 Summer '10
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 Graph Theory, ways, nonnegative integers, nonnegative integers corresponds

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