4 gentlemen and 4 ladies are to be seated at | vedclass

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Question

(D) Total number of ways to arrange $8$ people at a round table is $(8-1)! = 7!$.To seat them alternately,first arrange the $4$ gentlemen at the round

Vedclass · Accepted Answer

$1/35$

Vedclass · Answer

(D) Total number of ways to arrange $8$ people at a round table is $(8-1)! = 7!$.To seat them alternately,first arrange the $4$ gentlemen at the round table in $(4-1)! = 3!$ ways.There are $4$ gaps created between the gentlemen,where the $4$ ladies can be seated in $4!$ ways.Thus,the number of favorable outcomes is $n(E) = 3! 	imes 4!$.The probability $P(E) = \frac{n(E)}{n(S)} = \frac{3! 	imes 4!}{7!} = \frac{6 	imes 24}{5040} = \frac{144}{5040} = \frac{1}{35}$.

$4$ gentlemen and $4$ ladies are to be seated at a round table. What is the probability that they sit alternately?

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