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?
.	Choose the correct answer: A) 172000 B) 12600 C) 45920 D) 43200 E) 54200
Start with the 4 people who want to face forward - for the first one, there are 5 options, for next one, 4 options and so on till we get 5*4*3*2.   Next, go on to 3 people who want to face back - for the first one, there are 5 options, for the next one, 4 options and so on till we get 5*4*3.   Now, we have 3 seats leftover and 3 indifferent people who can be arranged in 3*2*1 ways.   All in all, we can arrange 10 people in 5*4*3*2*5*4*3*3*2*1 = 14400 * 3= 
<gadget id="calculator">14400 * 3</gadget>
<output>43_200</output>
43200   Answer (43200)
<result>D</result>
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?
.