Math 101.01
In-Class assignment #2
Due 12:01 p.m. Thursday, 4 February, 1999
On a separate piece of paper, answer the following questions.
Neatness counts. Label your dang answers!!!
1.
An ice-cream parlor has a make-it-yourself sundae. The sundae includes a choice among 20 flavors of ice cream,
5 types of toppings (e.g. hot fudge, caramel), and 10 assorted varieties of sprinkles (e.g. peanuts, marshmallow,
chocolate drops). A typical sundae consists of 1 flavor ice cream, one topping and only 1 of the assorted
sprinkles. How many different sundaes are possible?
2.
Suppose that the deeeluxe sundae at the above mentioned ice-cream parlor consists of 3 flavors of ice cream
(repeats allowed), 2 toppings (repeats not allowed), and 3 of the assorted sprinkles (repeats allowed). How many
deeeluxe sundaes are possible?
3.
Yesterdog's House of Hot Dogs & Nostalgia (YHHDN for short) will open soon, but first it must print its menus.
Suppose that on the Ultra-dog hot dog a customer must choose exactly 5 different toppings from the 15 possible
toppings.
a. How many different Ultra-dogs are possible?
b. Now suppose that the customer may choose at most 3 different toppings from the 15 possible. How many
different Ultra-dogs are possible? (Hint: Determine the number with 1 topping, with 2 toppings, etc.)
4.
Five-card draw is the classic poker game. On the first deal each player gets 5 cards. The player can arrange them
in any way desired.
a. How many different 5-card hands are possible?
b. How many hands will contain exactly 4 eights?
c. How many hands will contain exactly 3 eights?
d. How many hands will contain 3 aces and 2 eights?
e. How many hands will contain 4 of a kind (any kind)? (Hint: determine the number of hands which contain 4
aces, 4 twos, 4 threes, etc.)
f. What is the probability of being dealt a hand that contains 3 aces and 2 eights on the first deal?
g. What are the odds of being dealt a full house on the first deal?
5.
Suppose that a typical date in Ellensburg consists of going on a hike, then to the movies and then to a coffeehouse.
There are three good hiking trails, two movies theatres showing a total of 7 movies a week and there are 6
coffeehouses (not counting the 7-11's) in town. How many different typical dates are possible in a week? (Dates
in which you do the same set of activities but with a different person do not count as different dates). And you
thought Ellensburg was boring.
6.
Suppose you have 6 CD's in your CD player. The first, third, and fourth CD's have 8 songs. The second and fifth
CD's have 7 songs, and the sixth CD has 12 songs. If your CD player is set on shuffle, how many different 5 song
sets are possible if
a. Your CD player repeats songs
b. Your CD player doesn’t repeat songs
7.
Suppose that you own 95 CD's, how many ways can you choose 6 of them to load into your player?
8.
A combination lock has 35 numbers on the dial. How many 3 number combinations are possible if no number in
the combination may be used more than once? Should the lock be called a "combination lock" or a "permutation
lock"? Can you envision yourself calling it a "permutation lock"?
9.
To subscribe to the electronic version of ESPN, The Magazine, you need to choose an 8-character password. The
password may contain letters or numbers 0-9. How many different passwords are possible?
10. What is the probability that a word chosen at random from this sentence is the word “the”?