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- bobbym
- 2012-12-18 11:37:13
Hi;
I agree.
- scientia
- 2012-12-18 11:30:56
bobbym wrote:
You can't do that as that allows for possibilities in which there's a girl at both ends
Not at the same time!
Exactly. Jacks's method allows girls to be at boths ends at the same tiem – that was where his proof went wrong.
He wanted us to tell him where his proof went wrong, didn't he?
- bobbym
- 2012-12-18 11:19:42
Hmmmm. I know that. I know that you kid but you do not joke.
- anonimnystefy
- 2012-12-18 11:15:45
I was just kidding!
- bobbym
- 2012-12-18 11:14:42
Point is, sometimes it is a guy and sometimes it is not. Depending on what slot the last guy goes into.
- anonimnystefy
- 2012-12-18 11:10:53
Well, maybe the girls at the ends are in a superposition and our observation force the situation to enter one of the two possible states. 
- bobbym
- 2012-12-18 11:07:45
You can't do that as that allows for possibilities in which there's a girl at both ends
Not at the same time!
- jacks
- 2012-12-18 04:42:01
Thanks bobbym and scientia.
but i did not understand the meaning of
You can't do that as that allows for possibilities in which there's a girl at both ends
- scientia
- 2012-12-18 03:11:10
jacks wrote:
But where i have done mistake in my solution.
Your mistake is in
jacks wrote:
now arrange girls in 7 gaps ,
You can't do that as that allows for possibilities in which there's a girl at both ends, which you don't want. The possibilities are either
X_X_X_X_X_X_
or
_X_X_X_X_X_X
Each set has ways; hence there are ways altogether.
- bobbym
- 2012-12-18 03:06:22
Arrange the girls first in a line;
_ G _ G _ G _ G _ G _ G _ = 6!
In the first _ 6 boys can go
_ G (6 boys ) G _ G _ G _ G _ G _
In the second 5 boys
_ G (6 boys ) G (5 boys ) G _ G _ G _ G _
all the way down to
_ G (6 boys ) G (5 boys ) G (4 boys) G (3 boys) G (2 boys) G _
That can be done in 6 x 5 x 4 x 3 x 2 = 6!
So far we have 6! * 6!, now the last two slots
_ G (6 boys ) G (5 boys ) G (4 boys) G (3 boys) G (2 boys) G _
the one remaining boy can go in 2 ways.
2 * 6! * 6!
- jacks
- 2012-12-18 02:56:01
Yes bobbym you are right.
But where i have done mistake in my solution.
- bobbym
- 2012-12-18 02:49:35
Hi;
I am getting 2 * 6! * 6! as the answer. Provided we are assuming the girls and boys are distinct which is reasonable.
- jacks
- 2012-12-18 02:35:52
6 boys and 6 girls are sitting in a row . Then the no. of ways that boys and girls sits alternatively
my solution::
Using gap method::
here X = denote boys and _ = denote girl
Then X _ X _ X _ X _ X _ X _
first we can arrange boys , which can be done in 6! ways
now arrange girls in 7 gaps ,
for that first we select 6 place out of 7 which can be done in C (7,6) ways and now arrange these 6 girls
Which can we done in C(7,6) * 6! = 7!
So total no. of ways is = 6! * 7!
but answer is = 2*6! *6!
so where i have done mistake
Thanks