A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

sh3lsh

  • one year ago

Stars 'n' bars Theorem Problem. 1. A bagel shop has 8 kinds of bagels. How many ways to buy a dozen bagels? 2. A bagel shop has 8 kinds of bagels. How many ways to buy a dozen bagels, with at most 4 onion and at most 2 poppy seed?

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do you know Combinations and Permutations

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    12C1 +12C2 +12C3+...12C8

  3. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh, are you sure? I know the answer for both problems, I'm just looking for the methods. The first solution should have k=4;n=8 .

  4. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    are these your answers 50388 and 35846?

  5. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Let me run it through Wolfram Alpha, I just have the combinatoric form.

  6. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Unfortunately, no to the first one. I have 11C4, which is 165. For the second, it was correct!

  7. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    35846 is correct but 50388 is not?

  8. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Honestly, perhaps I'm concluding the wrong answer for the first question, we didn't complete the problem to its entirety. I just have k =4; n=8, which in the stars n bars theorem is just (10 choose 8). Perhaps it meant something else.

  9. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    We just wrote that 8 bagels were determined, so the question boiled down to x1+x2...+x8=4

  10. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    shouldn't you have \[{8-1+12\choose 8-1}\] or \[{8-1+12\choose 12}\]

  11. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    if you are using stars and bars

  12. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    My understanding that it's a little different with a lower and upper bound. I don't understand the concepts yet to agree nor disagree with what you wrote.

  13. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you have 8 different bagels ||||||| the bars make 8 possible locations or bagels 1||||||| |2|||||| ||3||||| |||4|||| ||||5||| |||||6|| ||||||7| |||||||8

  14. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    let xxxxxxxxxxxx be the bagels

  15. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you want to arrange |||||||xxxxxxxxxxxx

  16. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the above is an example of all 12 bagels of the same kind (the 8th kind of bagel)

  17. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the number of ways to arrange it is \[{7+12\choose 7}={8-1+12\choose 8-1}\]

  18. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    anyway...the number of ways to do problem 1 has to be larger than the number of was to do #2

  19. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    since we are putting on a restriction

  20. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ah! Okay!

  21. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You're correct, I wrote my response referring a different question. I agree with what you wrote!

  22. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so you know how to get the 35846

  23. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ?

  24. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I know how to get the first answer. For the second, would we use the inclusion - exclusion principle?

  25. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  26. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    All Solutions - solutions with x> 4 - solutions with y> 2 + intersection where (x> 4 and y> 2)? How do I find all solutions?

  27. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that is it we already did...\[{8-1+12\choose 8-1}=50388 \]

  28. sh3lsh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That's obvious. I don't even know why I asked that question. I got it from here , you're the bomb. Thanks so much.

  29. Zarkon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no problem

  30. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.