What is the most efficient way to approach the following problem:
Seven men and seven women have to sit around a circular table so that no 2 women are together. In how many different ways can this be done?
a)3
b)4
c)6
d)12
e)24
Seating arrangemen ts
This topic has expert replies
- Neo2000
- Legendary Member
- Posts: 519
- Joined: Sat Jan 27, 2007 7:56 am
- Location: India
- Thanked: 31 times
As women have to sit in-between the men, arrange the men first
7 men can be arranged around a circular table in 6! ways
Now, there are 7seats for 6 women to sit in. They can sit in 7P6 ways
Therefore total number of ways = 6! x 7P6
7 men can be arranged around a circular table in 6! ways
Now, there are 7seats for 6 women to sit in. They can sit in 7P6 ways
Therefore total number of ways = 6! x 7P6
Can you help me understand your response. Why can 7 men not be arranged in 7! ways. Any why do you say for 6 women to sit in when the question says there are 7 women? I'm just trying to understand the logic. Thanks for your help.
- Neo2000
- Legendary Member
- Posts: 519
- Joined: Sat Jan 27, 2007 7:56 am
- Location: India
- Thanked: 31 times
You are arranging them around a circular table
The number of ways of arranging "n" things around a circle in (n-1)!
However, once the men have been arranged, its no longer a circular arrangement. You now have 7 empty places and 6 women to fill in those places
The number of ways of arranging "n" things around a circle in (n-1)!
However, once the men have been arranged, its no longer a circular arrangement. You now have 7 empty places and 6 women to fill in those places
This seems highly inaccurate given that the largest answer choice is 24.Neo2000 wrote:Crap! i read the Q as 7men and 6women
So 7men can be arranged around a table in 6! ways and there are 7 places for 7women to sit between the men = 7! ways
Your final answer has to be 6! x 7!
6! x 7! = 720 * 5040 = a seven digit number. You're suggesting that there are over 3.6 million ways to do this? hmm.... i don't know the answer but i don't think that's right.
- Neo2000
- Legendary Member
- Posts: 519
- Joined: Sat Jan 27, 2007 7:56 am
- Location: India
- Thanked: 31 times
https://www.tutorvista.com/content/math/ ... ations.php
The last bit on the page confirms my approach.
The last bit on the page confirms my approach.