Good explanation but accordingly to the post the answer is 9

The question is little hard as you have nested restriction. I found easier to count it physically as the number 4 is small

Let us say that the four tracks are 1 2 3 4; Now no train should be on the original track, so the track 1 should have train number 2, 3, or 4. If track 1 has train number 2, then track 2 should have either track either train 1, 3, or 4; if track 1 has train number 2 and track 2 contains train 1, then only possibility for track 3 and track 4 is train 4 and train 3

So the possible sequences are with track 1 having train number 2 are 2, 1, 4, 3; 2, 3, 4, 1; 2, 4, 1, 3; So 3 possibilities.

Using similar logic for other possibilities

So the possible sequences are with track 1 having train number 3 are 3, 1, 4, 2; 3, 4, 2, 1; 3, 4, 1, 2; So 3 possibilities.

So the possible sequences are with track 1 having train number 4 are 4, 1, 2, 3; 4, 3, 1, 2; 4, 3, 2,1 ; So 3 possibilities.

In total 9 ways

For counting questions where the answer choices are pretty small, you should definitely consider LISTING all of the possible outcomes (as rapsjade does above).

For more on this see:

I agree with your answer. My bad. I excluded only the case where all the trains were in their respective tracks, i.e Train 1 in track 1 and Train 2 on track 2.....

However the questions states that no train should be on its original track.

Manually counting seems to be the best method applicable.

Regards,

I agree with the last post.

The question is not the top-notch. Moreover, what is not explicitly stated in the question should not be inferred. OR at most to some extent

Solution
This is a classic derangement problem. A derangement is a permutation in which no element appears in its original position.

The number of derangements of $n$ elements is given by:

D(n) = n! * (1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!)

For n = 4, we compute:

D(4) = 4! * [1 - 1/1! + 1/2! - 1/3! + 1/4!]
D(4) = 24 * [1 - 1 + 1/2 - 1/6 + 1/24]
D(4) = 24 * [1 - 1 + 12/24 - 4/24 + 1/24]
D(4) = 24 * [1 - 1 + 9/24]
D(4) = 24 * 9/24
D(4) = 9

Answer: (c) 9