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. 172000

B. 12600

C. 45920

D. 43200

Answer: Option D

Solution(By Examveda Team)

The four person who wish to sit facing forward can be seated in: ⁵P₄ ways and 3 who wish to sit facing towards the rear can be seated in: ⁵P₃ ways and the remaining 3 can be seated in the remaining 3 seats in ³P₃ ways.
Total number of ways
= ⁵P₄ × ⁵P₃ × ³P₃
= 43200