0

Question -In how many ways can eight people be seated around the table if two people insist on sitting next to each other?

Since the position of two people are known , i thought the answer would simply be 6!. Am i right teachers because i still have doubts.

Dave
  • 43

1 Answers1

0

Note that two people seating together is considered to be one element. Hence, the number of ways of seating $7$ people at a round table: $$(n-1)! = 6! = 720$$ But, we can arrange the two people also in $2!=2$ ways, giving us a total of: $$720\times 2 = 1440 \text{ ways} $$

  • How about the row problem with the same question sir? – Dave Jan 01 '18 at 07:54
  • @Dave Then there are $7!\times 2$ ways, right? Because there are $n!$ ways of seating $n$ people on a row.. –  Jan 01 '18 at 07:55
  • Why would you consider two people sitting together be an element?wouldnt it be 2! just like in word problems? – Dave Jan 01 '18 at 07:58
  • Sorry but can i debate alittle bit more sir? – Dave Jan 01 '18 at 08:09
  • Lets review the row problem again sir. By sitting next to each other, two seat have already been taken which left only six seat. So we have 6! ×2? – Dave Jan 01 '18 at 08:09
  • I hope you know that we can arrange n people in a row in $n!$ ways. I feel that is clear for you. Now, we have 8 people who need to be arranged in a row with 2 people insisting that they should sit next to each other. –  Jan 01 '18 at 08:13
  • Now, for the purpose of calculation, assume they are an inseparable element (but two people, say, A and B). Then, we have 7 elements. Thus can be arranged in 7! ways. But, while sitting, we can easily note the ordering AB is different from BA. This gives 2 ways to arrange the inseparable friends. This gives us: 7! * 2 ways. –  Jan 01 '18 at 08:16
  • I hv learnt nothing from my university and have to do online research to pass tutorial . Can i get your contact no. Sir? I want to give you a call from viber – Dave Jan 01 '18 at 08:42
  • @Dave The members of MSE generally do not give their personal details to anybody. –  Jan 01 '18 at 08:43
  • Okay.To be honest i have still doubts . I want to know why you use elements instead of chairs. By knowing two people position i thought 2 chairs have already been owned which left only 6 chairs for 6 people for their position. Why would you use 7! instead of 6 ! Sir? – Dave Jan 01 '18 at 08:46
  • I am always like that when it comes to maths. I want to know everything , sorry in advance sir. – Dave Jan 01 '18 at 08:55
  • See if this helps you: https://www.mbatious.com/topic/331/seating-arrangement-around-various-geometrical-figures –  Jan 01 '18 at 08:58