Now as there are 12 Stations out which Train has to be stopped at 4 stations so…
Let 1 2 3 4 5 6 7 8 9 10 11 12 ..these are the stations ...Out of them we have to take 4 stations such that they are non-adjacent now ..
At First count Non-Adjacent Places …Just Think..🤔…..
Suppose train stops at 4 non-adjacent …... so left stations are 8..
1 2 3 4 5 6 7 8….Now these 8 stations would help us to make that 4 stations non-adjacent …?
Here Non-Adjacent Places are marked as *
*1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 *
Yahoo!😁..there are 9 stars hence 9 non-adjacent...Out these 9 we have to select 4 stations ...as on stopping we get total 12 stations back…
Now Here should we apply Permutation or Combination??😩...No Worries ..
Let apply 9P4 ...but here 4 stations that are selected are in order...as Permutation takes first 4 non-adjacent places as 24 ways similar with all so to count once we divide by 4! …
9P4/4!= 9!/(5!*4!)==126
Or choose directly 9C4=126