There are 10 seats around a circular table. If 8 men and 2 women have to seated around a circular table, such that no two women have to be separated by at least one man. If P and Q denote the respective number of ways of seating these people around a table when seats are numbered and unnumbered, then P : Q equals?  Choose the correct answer:	A) 10:1	B) 9:1	C) 72:1	D) 8:1	E) None of these
Explanation :   Initially we look at the general case of the seats not numbered.The total number of cases of arranging 8 men and 2 women, so that women are together:⇒ 8×!2!The number of cases where in the women are not together:⇒9!−(8!×2!)=QNow, when the seats are numbered, it can be considered to a linear arrangement and the number of ways of arranging the group such that no two women are together is:⇒ 10!−(9!×2!)But the arrangements where in the women occupy the first and the tenth chairs are not favourable as when the chairs which are assumed to be arranged in a row are arranged in a circle, the two women would be sitting next to each other.The number of ways the women can occupy the first and the tenth position:=8!×2!The value of P =10!−(9!×2!)−(8!×2!)Thus P : Q = 10 : 1   10:1nswer : 10:1
<result>A</result>
There are 10 seats around a circular table. If 8 men and 2 women have to seated around a circular table, such that no two women have to be separated by at least one man. If P and Q denote the respective number of ways of seating these people around a table when seats are numbered and unnumbered, then P : Q equals?