School group
There are five girls and seven boys in the group. They sit in a row next to each other. How many options if no two girls sit next to each other?
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Dr Math
This problem is identical to saying if you have 7 boys in a row, how many ways are their to place 5 girls in that row without having two girls next to each other. you would have 8 locations to choose from.
B B B B B B B
+ B + B + B + B + B + B + B +
Here you have 8 places to arrange the girls and 5 girls. This is the same as 8 choose 5 which equals 56.
Then for each of those 56 arrangements, you can look at every possible arrangement of individual girls, the number of which is 5!
Lastly for each of those unique placement of girls, and unique order of gils, you can take the unique order of boys which would be 7!
In my calculation, the total should be 56 x 5! x 7! = 33868800
B B B B B B B
+ B + B + B + B + B + B + B +
Here you have 8 places to arrange the girls and 5 girls. This is the same as 8 choose 5 which equals 56.
Then for each of those 56 arrangements, you can look at every possible arrangement of individual girls, the number of which is 5!
Lastly for each of those unique placement of girls, and unique order of gils, you can take the unique order of boys which would be 7!
In my calculation, the total should be 56 x 5! x 7! = 33868800
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