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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.

#### 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