dutchp0wner wrote:
I don't get it.
I see how it should it be 2 instead of 7, but why does the formula of the bold not hold?
*B*B*B*B*B*B*
# of ways 6 girls can occupy the places of these 7 stars is 6C7;# of ways 6 girls can be arranged on these places is 6!;
# of ways 6 boys can be arranged is 6!.
7∗6!∗6!/12! = D
Im not allowed to post links but the title of the topic is: A row of seats in a movie hall contains 10 seats. 3 Girls[/qu
However , i understood the solution posted above by rest of users that in seat 1 - 6 boys can be seated, seat 2 -5 boys .. So , 6! ways boys can be seated . Similarly girls can be seated in 6! . Boys and Girls can be arranged in 2! ways
Probability =2x6!x6!/ 12!
What i don't understand is :-
We can assume all Girls are identical and boys are same. So , All 6 boys can be seated in 1 ways and rest 6 girls can be seated in 7 positions by 7C6 ways . So total no. of possible ways meeting constraint = 1x7C6x2= 14 ways
max. possible ways = ??
Probability = 14 / ??
Please correct my basic understanding ,where i am getting wrong.
Bunuel VeritasKarishma chetan2u Guys please help
bb Nirmesh83The girls are not identical and neither are the boys. People are all distinct. You need to arrange them. You have 12 distinct seats.
On seat 1, you can make a girl sit or boy sit. This will decide which seats get occupied by girls and which by boys. If a girl sits on seat 1, seats 3, 5, 7, 9 and 11 will be taken by girls and seats 2, 4, 6, 8, 10 and 12 will be taken by boys. Then you arrange the girls and the boys in their own 6 seats each.
I am not sure from where 7 comes in. This is what I can think of. Say you are arranging 6 boys in 6 distinct seats in 6! ways. Now there are 7 open spots around them.
__ B __ B __ B __ B __ B __ B __
Note that we are not allowed to pick any 6 of these 7 spots so 7C6 is incorrect. If we do 7C6, acceptable arrangements will include:
G B G B G B __ B G B G B G
G B __ B G B G B G B G B G
etc..
But this will mean 2 boys are sitting together. That is not allowed.
Whether we pick the first slot or not fixes all other slots for us. If we pick the first slot for a girl, we get:
G B G B G B G B G B G B
If we do not pick the first slot for a girl, we get
B G B G B G B G B G B G
These are the only two acceptable options.