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: Option C
Solution(By Examveda Team)
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 favorable 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
Related Questions on Permutation and Combination
A. 3! 4! 8! 4!
B. 3! 8!
C. 4! 4!
D. 8! 4! 4!
A. 7560,60,1680
B. 7890,120,650
C. 7650,200,4444
D. None of these
A. 8 × 9!
B. 8 × 8!
C. 7 × 9!
D. 9 × 8!
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