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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
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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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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Yes bobbym you are right.
But where i have done mistake in my solution.
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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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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But where i have done mistake in my solution.
Your mistake is in
now arrange girls in 7 gaps ,
X_X_X_X_X_X_
or
_X_X_X_X_X_X
Each set has
ways; hence there are ways altogether.Offline
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
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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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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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.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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I was just kidding!
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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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?
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Hi;
I agree.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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