Circular Permutation: 7 Boys 5 Girls

  • Context: Undergrad 
  • Thread starter Thread starter jxta
  • Start date Start date
  • Tags Tags
    Circular Permutation
Click For Summary

Discussion Overview

The discussion revolves around the problem of determining the number of circular arrangements of 7 boys and 5 girls, with the condition that no two girls sit adjacent to each other. The focus is on combinatorial reasoning and the implications of circular permutations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant presents an initial calculation suggesting that the total number of arrangements is 6! * P(7,5), leading to a result of 1,814,400, which they later claim is incorrect.
  • Another participant argues that the answer should be divided by 12 due to the nature of circular arrangements, asserting that the previously calculated answer of 252 is incorrect and provides an example of a non-circular configuration to illustrate their point.
  • A third participant proposes a formula involving (21 + 15) * 5! * 7! / 12, which they claim equals the previous participant's answer, indicating a potential agreement on the method but not necessarily on the final result.

Areas of Agreement / Disagreement

Participants express differing views on the correct approach to solving the problem, with no consensus reached on the final answer or the methods used. Multiple competing views remain regarding the calculations and the implications of circular arrangements.

Contextual Notes

There are unresolved assumptions regarding the treatment of circular permutations and the specific conditions under which arrangements are counted. The calculations presented depend on interpretations of the arrangement rules and may vary based on definitions used.

jxta
Messages
2
Reaction score
0
Circular Permutation??

if there are 7 boys and 5 girls, how many circular arrangements are possible if the ladies do not sit adjacent to each other.??
 
Physics news on Phys.org
welcome to pf!

hi jxta! welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 


tiny-tim said:
hi jxta! welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:

i think :-

boys ways;-(7-1)=6!
now there are 5 girls and 7 seats(in b/w boys) so there are P(7,5) number of ways, the girls can sit.
p(7,5)=7!/(7-5)!

i.e, total no. of ways= 6!*p(7,5)
= 6!*7!/(7-5)!
= 1814400 (but this ans is wrong).

ans = 252 (in my book)
 


you have to divide by 12 (and not 2 * 12 = 24 as you can not mirror) at some step, as it is a circular placement.

252 is definitely wrong, look at the following (non-circular) configuration:

B g B g B g B g B g B B

This gives us 5! * 7! = 604.800 possibilities. Divide by 12 gives 50.400 possibilities. So the answer must be greater than (or equal to) 50.400
 
Last edited:


My answer:

\frac{( 21 +15) \cdot 5! \cdot 7!}{12} = 1.814.400

(this equals you answer)
 
Last edited:

Similar threads

MHB Solving Permutations Question with Restrictions
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Understanding permutations and combinations in a coin toss experiment
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How Are Permutations Calculated in a Circular Seating Arrangement?
  • · Replies 2 ·
Replies
2
Views
2K
High School Seat arrangements around a rectangular table
  • · Replies 8 ·
Replies
8
Views
4K
MHB Permutation and Combination Homework Help
  • · Replies 5 ·
Replies
5
Views
5K
High School How are permutations and probability related?
  • · Replies 1 ·
Replies
1
Views
2K
High School Boy/girl riddle (conditional probability)
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad How to find the nth binary permutation?
  • · Replies 2 ·
Replies
2
Views
2K
Basic probability question (1 boy + 2 girls of a group of 7)
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How Many Permutations Exist Where M Equals K on Cards?
  • · Replies 31 ·
2
Replies
31
Views
3K