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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