Aptitude Discussion

Q. |
In a railway compartment, there are $2$ rows of seats facing each other with accommodation for $5$ in each, $4$ wish to sit facing forward and $3$ facing towards the rear while $3$ others are indifferent. In how many ways can the $10$ passengers be seated? |

✖ A. |
$172,000$ |

✖ B. |
$12,600$ |

✖ C. |
$45,920$ |

✔ D. |
$43,200$ |

**Solution:**

Option(**D**) is correct

The four person who wish to sit facing forward can be seated in: ${^5P_4}$ ways and $3$ who wish to sit facing towards the rear can be seated in: ${^5P_3}$ ways and the remaining $3$ can be seated in the remaining $3$ seats in ${^3P_3}$ ways.

Total number of ways $= {^5P_4} × {^5P_3} × {^3P_3}$

$=\textbf{43200}$