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#1 2012-12-18 02:35:52
- jacks
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boys and girls
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
#2 2012-12-18 02:49:35
- bobbym
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Re: boys and girls
Hi;
I am getting 2 * 6! * 6! as the answer. Provided we are assuming the girls and boys are distinct which is reasonable.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#4 2012-12-18 03:06:22
- bobbym
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Re: boys and girls
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!
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#5 2012-12-18 03:11:10
- scientia
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Re: boys and girls
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.
#7 2012-12-18 11:07:45
- bobbym
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Re: boys and girls
You can't do that as that allows for possibilities in which there's a girl at both ends
Not at the same time!
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#8 2012-12-18 11:10:53
- anonimnystefy
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Re: boys and girls
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. 
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#9 2012-12-18 11:14:42
- bobbym
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Re: boys and girls
Point is, sometimes it is a guy and sometimes it is not. Depending on what slot the last guy goes into.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#10 2012-12-18 11:15:45
- anonimnystefy
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Re: boys and girls
I was just kidding!
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#11 2012-12-18 11:19:42
- bobbym
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Re: boys and girls
Hmmmm. I know that. I know that you kid but you do not joke.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#12 2012-12-18 11:30:56
- scientia
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Re: boys and girls
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?
#13 2012-12-18 11:37:13
- bobbym
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Re: boys and girls
Hi;
I agree.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.