Permutation-Combination
Aptitude

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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.

$43,200$

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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 $= {^5P_4} × {^5P_3} × {^3P_3}$

$=\textbf{43200}$


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