HW3 Solutions
Dilip Raghavan
September 21, 2008
1
Section 5.3
Problem 11.
First choose the 2 kinds of fruit. Since there are 5 kinds, there are
5
2
ways to do this. Now
we want to select 10 objects from 2 kinds of objects, making sure that there is atleast one of each kind (we
can’t have all the fruits be of the same kind because we need
exactly two
kinds). So we first select one fruit
of each kind. Now we need to select the remaining 8 fruits from 2 kinds of fruit. There are
8
+
2

1
8
ways
to do this. So the answer is
5
2
×
8
+
2

1
8
.
Problem 12.
The best way to deal with the pink, lavender and tan balls is to break into cases depending on
exactly how many of those balls we choose. So there are 4 cases.
•
Case I: We don’t choose any of the pink, lavender and tan balls. This means that we must select 8
balls from 3 kinds of balls (red, white and blue). There are
8
+
3

1
8
ways to do this.
•
Case II: We choose exactly one out of the pink, lavender and tan balls:
3
1
ways. Now we choose 7
balls from 3 kinds:
7
+
3

1
7
ways. So a total of
3
1
×
7
+
3

1
7
ways.
•
Case III: Choose exactly two out of the pink, lavender and tan balls:
3
2
ways. Now choose 6 balls
from 3 kinds:
6
+
3

1
6
ways. So the total is
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 Spring '11
 Hernandez/Rag
 Want, Binary relation, Walk This Way, kind

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