Probability Q7

7..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

	A.	9 : 1
	B.	72 : 1
	C.	10 : 1
	D.	8 : 1

Answer – (C)
Solution:
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!)=Q
Now, 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