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  • There are 7 seats in a row. Three persons take seats at random. The probability that the middle seat is always occupied and no two persons are consecutive isOpti

There are 7 seats in a row. Three persons take seats at random. The probability that the middle seat is always occupied and no two persons are consecutive is

Option: 1

\frac{9}{70}


Option: 2

\frac{9}{35}


Option: 3

\frac{4}{35}


Option: 4

None of these


Answers (1)

best_answer

\begin{aligned} & \mathrm{n(S)={ }^7 C_3 \times 3 !=\frac{7 \cdot 6 \cdot 5}{6} \cdot 6=210 }. \\ \\& \mathrm{n(E)={ }^2 C_1 \times{ }^2 C_1 \times{ }^1 C_1 \times 3 !} \end{aligned}

because one has to sit at any one of the two marked seats on the left and the other has to sit at any one of the two marked seats on the right.

\mathrm{\therefore \quad P(E)=\frac{n(E)}{n(S)}=\frac{2 \times 2 \times 6}{210}=\frac{4}{35}}

Posted by

Sayak

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