174
Solutions to Exercises
First die
17. (a) Here are the possibilities. There are five ways to get a S::;"econ=d:dc:iet::t=+:+:::t:::
total of eight.
(b) Here are the possibilities. There are six ways to get a
total of seven.
(c) There are 5
+
6
=
11 ways to get an eight or a seven.
First die
Second die
6
1
(d) Getting doubles means two l's, two 2's, two 3's, two 4's, two 5's or two 6's. There are six ways
to get doubles.
19. (a) 6 x 6
=
36;
(b) 6
5
=
7776;
(d) Since there are
6
n
ways in which the dice can land and in precisely six of these ways the dice all
land the same, the answer is
6
n

6.
20.
(a)
[BB]
HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH,
THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT.
There are 16 possibilities in all.
(b) 4 ways;
(b) 6 ways;
(c) 4 ways;
(d) 4
+
6
+
4
+
1
=
15 ways.
21. (a) 9 ·10·10·10·10
=
90,000;
(b) 9·9·8·7·6
=
27,216;
(c) 9000027216
=
62,784.
22. (a) [BB] 26 x 26 x 26 x 10 x 9 x 8
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 Summer '10
 any
 Graph Theory, Meal, ways, Main course, Hors d'œuvre, two L

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