gaokao 2015 Q17

gaokao · China · sichuan-arts Probability Definitions Combinatorial Counting (Non-Probability)
17. (This question is worth 12 points)
A minibus has 5 seats numbered $1,2,3,4,5$. Passengers $P _ { 1 } , P _ { 2 } , P _ { 3 } , P _ { 4 } , P _ { 5 }$ have assigned seat numbers $1,2,3,4,5$ respectively. They board in order of increasing seat numbers. Passenger $P _ { 1 }$ did not sit in seat 1 due to health reasons. The driver then requires the remaining passengers to be seated according to the following rule: if their own seat is empty, they must sit in their own seat; if their own seat is occupied, they can choose any of the remaining empty seats. (1) If passenger $P _ { 1 }$ sits in seat 3 and other passengers are seated according to the rule, there are 4 possible seating arrangements. The table below shows two of them. Please fill in the remaining two arrangements (enter the seat numbers where passengers sit in the blank cells);
(2) If passenger
Passenger$P _ { 1 }$$P _ { 2 }$$P _ { 3 }$$P _ { 4 }$$P _ { 5 }$
\multirow{3}{*}{Seat Number}32145
32451

$P _ { 1 }$ sits in seat 2, and other passengers are seated according to the rule, find the probability that passenger $P _ { 5 }$ sits in seat 5.
\section*{17. (This question is worth 12 points)}
A minibus has 5 seats numbered $1,2,3,4,5$. Passengers $P _ { 1 } , P _ { 2 } , P _ { 3 } , P _ { 4 } , P _ { 5 }$ have assigned seat numbers $1,2,3,4,5$ respectively. They board in order of increasing seat numbers. Passenger $P _ { 1 }$ did not sit in seat 1 due to health reasons. The driver then requires the remaining passengers to be seated according to the following rule: if their own seat is empty, they must sit in their own seat; if their own seat is occupied, they can choose any of the remaining empty seats. (1) If passenger $P _ { 1 }$ sits in seat 3 and other passengers are seated according to the rule, there are 4 possible seating arrangements. The table below shows two of them. Please fill in the remaining two arrangements (enter the seat numbers where passengers sit in the blank cells);\\
(2) If passenger

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
Passenger & $P _ { 1 }$ & $P _ { 2 }$ & $P _ { 3 }$ & $P _ { 4 }$ & $P _ { 5 }$ \\
\hline
\multirow{3}{*}{Seat Number} & 3 & 2 & 1 & 4 & 5 \\
\hline
 & 3 & 2 & 4 & 5 & 1 \\
\hline
 &  &  &  &  &  \\
\hline
 &  &  &  &  &  \\
\hline
\end{tabular}
\end{center}

$P _ { 1 }$ sits in seat 2, and other passengers are seated according to the rule, find the probability that passenger $P _ { 5 }$ sits in seat 5.