Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Yamasini

6 friends (Andy, Bandy, Candy, Dandy, Endy and Fandy) are out to dinner. They will be seated in a circular table (with 6 seats). Andy and Bandy want to sit next to each other to talk about the Addition Principle, Bandy and Candy want to sit next to each other to talk about the Principle of Inclusion and Exclusion. How many ways are there to seat them? Clarification: Rotations are counted as the same seating arrangements, reflections are counted as different seating arrangements.

  • one year ago
  • one year ago

  • This Question is Open
  1. hba
    Best Response
    You've already chosen the best response.
    Medals 1

    Circle (n-1)! Line n! Necklace or garland (n-1)!/2

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

    720.....

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

    proof: For the first seat, we have a choice of any of the 6 friends. After seating the first person, for the second seat, we have a choice of any of the remaining 5 friends. After seating the second person, for the third seat, we have a choice of any of the remaining 4 friends. After seating the third person, for the fourth seat, we have a choice of any of the remaining 3 friends. After seating the fourth person, for the fifth seat, we have a choice of any of the remaining 2 friends. After seating the fifth person, for the sixth seat, we have a choice of only 1 of the remaining friends. Hence, by the Rule of Product, there are 6*5*4*3*2*1=720 these 6 people. More generally, this problem is known as a Permutation. There are |dw:1358685675757:dw| ways to seat people in a row.

    • one year ago
    • Attachments:

See more questions >>>

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.