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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 VCRs, 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 cant be in the

same genre? (You cant 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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