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This is just a sketch of the solution to some of the problems from the review sheet which are not
covered in the back of the book.
Chapter 7 review, problem 6
: There are
(
4
3
)
choices for the three kings, and
(
48
2
)
choices for
the two nonkings, for a total of
(
4
3
)(
48
2
)
.
Chapter 7 review, problem 8
: There are
(
12
3
)
choices for which three people go in group
A
,
(
9
3
)
choices for which three people go in group
B
, and so on, for a total of
(
12
3
)(
9
3
)(
6
3
)(
3
3
)
. If the groups
do not have names, then we need to divide by 4! because there are 4! diﬀerent ways the groups can
be ordered.
Chapter 7 review, problem 16
: (a): Repetition is allowed (you can get the same kind of gum
more than once), and order doesn’t matter (you’re just buying 10 balls).
n
= 7 and
r
= 10, so the
answer is
(
16
10
)
.
(b): We assign three balls to red, leaving 7 balls for the remaining 6 colors. Answer:
(
12
7
)
.
(c): We assign one to each color, leaving 3 balls to be split among 7 colors. Answer:
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 Spring '08
 JUANG
 Signal Processing

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