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October 4th, 2016, 04:51 PM  #1 
Newbie Joined: Oct 2016 From: Canada Posts: 1 Thanks: 0  Permutations Help
Hello, I'm stuck on the following problem and am hoping for some guidance: For part (a), I believe the answer should be 10!. For (b, i), I'm thinking I should do 10*9*8*7*6*5 for distributing the 10 seats about the 6 people there, giving 151,200. It's at (b, ii) that I get stumped. At first I was thinking of putting the 3 friends together (which can be done in 3! ways). Then, because I put the 3 friends together, I would have 3 other friends left, so 3+1 = 4 groups. Among these 4 groups, the 8 seats can be distributed by 8*7*6*5. When I multiple 3!*8*7*6*5 together, I get 10,080, which is nowhere close to the correct answer of 33,600. I would really appreciate it if someone could tell me where I'm going wrong. Thank you! 
August 7th, 2017, 08:36 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,051 Thanks: 1395 
Do you still need help on this?

August 8th, 2017, 12:50 AM  #3  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,353 Thanks: 464 Math Focus: Yet to find out.  Quote:
The remaining 3 friends can sit in any of the other seats. i.e., the first friend can choose to sit in any 7 seats, the second can choose from 6 seats and the third from 5 seats. There are (70)(71)(72) = 210 ways they can be seated. Altogether, there are 8*20*210 = 33600 ways. Last edited by skipjack; August 8th, 2017 at 03:51 AM.  

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