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  • 4 gentlemen and 4 ladies take seats at random round a table. The probability that they are sitting alternately isOption: 1 <img alt="\frac{4}{35}" sr

4 gentlemen and 4 ladies take seats at random round a table. The probability that they are sitting alternately is

Option: 1

\frac{4}{35}


Option: 2

\frac{1}{70}


Option: 3

\frac{2}{35}


Option: 4

\frac{1}{35}


Answers (1)

best_answer

\mathrm{n(S)=7 !, n(E)=(3 !) \times(4 !)}

(\because after making 4 gentlemen sit in 3 ! ways, 4 ladies can sit in 4 ! ways in between the gentlemen)

\mathrm{\therefore \quad P(E)=\frac{(3 !) \times(4 !)}{7 !}=\frac{6}{7 \times 6 \times 5}=\frac{1}{35} .}

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Sayak

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