Finite Math Quiz 2 –Enumeration

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  Finite Math Quiz2–Enumeration Readthe followingscenariosand

determinewhichmethodwouldbethebestapproachtosolvetheproblem.  1. A coach
need
s to select 15 sen

iors to play on
the football team.   How many

diff

erent ways can

the coach select the team if 37 seniors try out?
a)Combinationb) Permutation c) Ruleof Product   3. A fighting game has

12 different fighters to choose

from.  The player then fights the remaining 11 characters in random order.  How many sequences of fights are possible?  
a) Combination b) Permutation c) Rule of Sum   5. A sales represen
tative has to visit 7 different clients and can choose to visit them in any order.  
How many different routes can the sales representative take
? a) Combination b) Permutation c) Rule of Sum   2. A fast food
restaurant has 12 combo meals.  
Each
combo meal has 7 options
for a side dish, 5 types
 of drink, and is ava
ilable in 2 sizes
 (“Regu
lar” or “La
rge”
).  
How many different combo meals can be purchased?
 a)Combination b) Ruleof Productc) Ruleof Sum  4. A used
video
store has 35 kung
-­‐

fu movies, 73 dramatic movies, 27 musicals, and 43 sci-­‐fi movies.   How many total videos are available for purchase?  
a) Combination b) Ruleof Productc) Ruleof Sum  6. How many different values
can be represented by two bytes?   Note a byte consists of a sequence of 8 bits, with each bit capable of storing one of two values (0 or 1).  a) Permutation with replacement
b) Permutation without replacement c) Permutationof non-­‐distinctelements     Computethe followingpermutationsandcombinations:  7. P(15,6
)     9.C(10,8
)     8. P(13,5
)   10. C(18,17
)    Read the following problems and compute the number of possibilities.   Partial credit is available only if work is shown. 11. How many different 5-­‐card poker hands containing only Diamonds are possible?
    12. The North American Numbering Plan (NANP) has established a special protocol for how area codes are numbered.   The first digit of an area code can be any of the numbers 2-­‐9, while the second and third digit can be any of the numbers 0-­‐9.   How many area codes can be generated in this way?
    13. A certain state uses the following rules to create license plates: Two letters followed by three digits. How many possible license plates can be created using those rules?
    14. A particular leve
l of a tower defense game requires you to place 10 towers that enemies will attempt to pass in order.  There are 3 red towers, 5 grey towers, and 2 green towers to choose from for this
level.   How many different arrangements of towers are possible?
    15. A campus coffee shop offers 15 types of hot beverage (coffee, tea, etc.), 8 varieties of sandwich, 12 types of cold beverage (soda, energy drinks, juice) and 11 different types of bagel.                                                                                                                                                                                How many different meals could be purchased if you wanted either a hot beverage and a bagel, or a cold beverage and a sandwich?
    16. A puzzle requires you to find a correct three-­‐color code using only three colors: Red, Blue, and Yellow.  Any color may be placed in any or all of the three positions. How many possible combinations are there?
    17. A travel app will suggest 3 hotels and 5 restaurants at random for any city it has information.   How many different suggestions can it make for a town that only has 8 hotels and 18 restaurants?
    18. In the World Series, the American League Champion plays the National League Champion. How
many World Series match-­‐ups are possible if there are 14 teams in the American League and 16 teams in the National League?
 

19. Characters in a Roman-­‐style game are assigned a name in the Tria Nomina style: which is

Praenomina (first name) Nomen (middle name) Cognomen (last name). There are only about 17

common Praenomina, but 130 Nomen and 193 common Cognomen. How many unique character names can be generated?

20. How many different ways can you arrange 15 billiard balls in a triangular rack?

Finite

Math

Quiz 2 –Enumeration

Read the following scenarios and determine which method would be the best approach to solve the

problem.

1. A coach needs to select 15 seniors to play on the football team. How many different ways can the coach select the team if 37 seniors try out?

a) Combination

b) Permutation

c) Rule of Product

3. A fighting game has 12 different fighters to choose from. The player then fights the remaining 11 characters in random order. How many sequences of fights are possible?

a) Combination b) Permutation c) Rule of Sum