There are 12 intermediate stations between two places A and B. Find the number of ways in which a train can be made to stop at 4 of these intermediate stations so that no two stopping stations are consecutive?
Examples –
Input : n = 12, s = 4 Output : 126 Input : n = 16, s = 5 Output : 792
# Python code to calculate number # of ways of selecting \'p\' non # consecutive stations out of # \'n\' stations def stopping_station( p, n): num = 1 dem = 1 s = p # selecting \'s\' positions # out of \'n-s+1\' while p != 1: dem *= p p-=1 t = n - s + 1 while t != (n-2 * s + 1): num *= t t-=1 if (n - s + 1) >= s: return int(num/dem) else: # if conditions does not # satisfy of combinatorics return -1 # driver code num = stopping_station(4, 12) if num != -1: print(num) else: print("Not Possible") # This code is contributed by "Abhishek Sharma 44" |
Output :
126
Please refer complete article on Number of stopping station problem for more details!
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