Circular Permutation?? if there are 7 boys and 5 girls, how many circular arrangements are possible if the ladies do not sit adjacent to each other.??
welcome to pf! hi jxta! welcome to PF! Show us what you've tried, and where you're stuck, and then we'll know how to help!
Re: welcome to pf! i think :- boys ways;-(7-1)=6! now there are 5 girls and 7 seats(in b/w boys) so there are P(7,5) number of ways, the girls can sit. p(7,5)=7!/(7-5)! i.e, total no. of ways= 6!*p(7,5) = 6!*7!/(7-5)! = 1814400 (but this ans is wrong). ans = 252 (in my book)
Re: Circular Permutation?? you have to divide by 12 (and not 2 * 12 = 24 as you can not mirror) at some step, as it is a circular placement. 252 is definitely wrong, look at the following (non-circular) configuration: B g B g B g B g B g B B This gives us 5! * 7! = 604.800 possibilities. Divide by 12 gives 50.400 possibilities. So the answer must be greater than (or equal to) 50.400
Re: Circular Permutation?? My answer: [tex]\frac{( 21 +15) \cdot 5! \cdot 7!}{12} = 1.814.400 [/tex] (this equals you answer)