permutation and combination problem
Probability
Level
2
the number of ways in which 6 men and 5 women can sit at a round table if no two women are to sit together is given by: A) 30 B) 5! 4! C) 7! 5! D) 6!*5!
The answer is 86400.
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1 solution
Using circular permutations, 6 men can be seated in a circle in ( 6 − 1 ) ! ways i . e . 5 ! ways. Now, there are 6 gaps between the 6 men that can be filled by 5 women in 6 ∗ 5 ∗ 4 ∗ 3 ∗ 2 = 6 ! ways. So, the required number of ways = 5 ! ∗ 6 ! = 8 6 4 0 0 w a y s