suryav wrote:

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

Here is another way to think about it - each seat is distinct. 5 face forward and 5 face back.

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 = 43200

Answer (D)

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Karishma

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