MasterPeeNice wrote:
RDhin wrote:
Total no. of arrangement can be 12! as we have total 12 people in a sitting arrangement
In this case we will fix the positions of boys and tend to fill the girls in those vacant positions, because even if two boys are together we can still having an arrangement with two Girls sitting around the corners
So girls can occupy can spot in the following arrangement
Girls . Boys. Girls . Boys. Girls . Boys. Girls . Boys. Girls . Boys. Girls . Boys. Girls .
total no. of arrangement in which girls can be filled is 7P6= 7!
total no. of arrangement in which boys can be filled is 6!
So total no. of arrangement in this case is 7!*6!
So Probability is 7!*6!/12! Option E
But this arrangement has a total of 7 seats occupied by Girls. There are only 6 Girls.
I agree that
12! is the total number of arrangements, so this goes in the denominator.
We also must agree that alternating seating Boy-Girl-Boy-Girl... (and Girl-Boy-Girl-Boy...) is the only way to avoid two girls seating next to each other. These are the 2 defined cases we need to permute: Boys sitting in odd seats, and boys sitting in even seats.
For case 1, up to 6 boys can take Seat 1. Any of 6 girls can take Seat 2. The number of available people in the second seat lowers by 1 to the end. So you have 6! boys times 6! girls.
Then you have to double the number for case 2, where a girl takes Seat 1 and boys take seat 2.
Therefore, option D seems correct.
That analogy of 6 boys and 6 girls starting with any boy or girl makes senses when we are asked when boys and girls sit alternatively.
However in this case question we are explicitly asked for cases when no two girls sit together, however two boys can sit together.
So arrangement like this
G. B. B. G. B. G. B. G. B. G. B. G
G = Girl and B = Boy
Is valid, it means net arrangements will be more then case discussed by you as 2 boys can even be sit together.
That seven position significance is that one position among them will be empty. And that makes two boys sit together as it is exemplified above.
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