Homework 2
Due: February 11, 2016
1. [1, 4.3.4] Your favorite ice cream shop only serves vanilla ice cream, but has 17 different
toppings to choose from.
(a) How many different sundaes are there with exactly 3 toppings?
(b) How many different sundaes are there with at least 2 toppings?
(c) How many different sundaes are there with no restriction on the number of toppings?
2. [1, 4.3.9] Suppose you live in Manhattan and your neighborhood looks like the image below.
(a) How many paths of shortest possible lengths (i.e. 13 blocks) are there from your
house to your work?
(b) Suppose the small circle is a coffee shop and you must stop there on your way to
work. How many paths (of shortest possible length) are there from your home to
your work that also stop by the coffee shop?
(c) Suppose that instead you are trying to save money and must avoid the intersection
where the coffee shop is at all costs - that way you only drink the coffee at work. Now
how many possible paths are there?
References
[1] Benedict Gross and Joe Harris. The Magic of Numbers. Pearson Prentice Hall, 2004.
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