Discrete Structure – hw

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CS191 Homework #9
Possible points:
Due Dec 7th, 2017
Name: ____________________________________ID No.: ______________________________
eMail Address:__________________________________________________________________
CS191 homework must be an individual e?ort. Make sure you do your own work. Clearly label your
output so I can follow what you are doing. Show all your steps.
1. Circuit City has a black Friday deal. You can choose one of 3 models of VCR’s, and
choose one movie from a selection of 10, and choose one universal remote from 4
options. How many choices are there?
2. A UMKC sweatshirt is offered with 3 different logos and 4 different colors. How many
sweatshirts are there to choose from?
3. The Spotify music service has 3 genres; country, rock and R&B. There are 6 songs in
country, 3 in rock, and 5 in R&B. How many different choices are available?
a. How many ways are there to choose a single song?
b. How many ways are there to choose a song from each genre? One from
country, one from rock and one from R&B?
c. How many choices are available if you choose 2 songs, and songs can’t be in the
same genre? (You can’t choose 2 in country or 2 in rock or 2 in R&B?)
d. How many choices are available if you choose 2 songs if you can choose the
same genre for both movies”
4. You can choose red, green, blue hat a red, green or blue shirt and a red, green or blue
pants.
a. How many outfits can you make with a green hat or a blue hat and red shirt?
b. How many outfits can you make with a blue hat or with red pants? ( Inclusion
Exclusion applies )
5. The 6 major Universities (UMKC, Stanford, MIT, UCM, Harvard, and Princeton) are
awarded consumer awards for 1st, 2nd and 3rd.
a. How many ways are there to choose the awards?
b. How many ways if UMKC has to get an award?
c. How many ways if UMKC and MIT have to get an award?
6. How many permutations are there for u, v, w, x, y, z?
7. How many combinations are there for u, v, w, x, y, z
8. Jobs, Gates, Joy, Knuth, and Hopper are going to be lined up to speak at a conference
(order matters).
a. How many ways can they be lined up?
b. How many ways if Jobs and Gates have to be together in that order?
c. How many ways if Jobs and Gates have to be together in any order ( Jobs then
Gates, or Gates then Jobs )
9. How many ways can you form a 4 person committee from 7 people?
10. How many ways can you order the letters of the words
a. break
b. startrek
c. aaabba
11. Implement Algorithm 6.4.9 (Generating Combinations) in the language of your choice.
Submit the source and sample input and output.
12. Implement Algorithm 6.4.14 (Generating Permutations) in the language of your choice.
Submit the source and sample input and output.
13. Expand (x + y)5 using the Binomial Theorem
14. Find the coefficients for the following terms using the Binomial Theorem
a. x3y8; (x+y)11
b. x2y4z4; (x+y+z)10
15. Show that if you roll a 20-sided die 21 times then you will get at least 2 die of the same
value.
16. Show that if you have 13 employees, then at least 2 will have a birthday in the same
month.
17. You pay your employees every 2 weeks. Show that some months they will get 3 checks.
18. People have choice of 5 tables in a restaurant.
a. How many people do you have to have before you know that 2 people are sitting
at the same table?
b. How many people do you have to have before you know that 4 people are sitting
at the same table?

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