CreationCarnage wrote:
If four trains are rerouted over tracks such that there is a train on every track and no train is on its original track, then how many ways can the trains be rerouted?
a) 4
b) 6
c) 9
d) 16
e) 24
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