Q53
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# coding=UTF-8
'''
There are exactly ten ways of selecting three from five, 12345:
123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
In combinatorics, we use the notation, 5C3 = 10.
In general,
nCr = n!/r!(n-r)!
,where r n, n! = n(n1)...321, and 0! = 1.
It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.
How many, not necessarily distinct, values of nCr, for 1 n 100, are greater than one-million?
'''
'''
Cn r+1 = Cn r * (n-r)/(r+1)
'''
MAX_EXCEED = 1000000
sum = 4
for n in range(24,101):
Cnr = n
count = 0
for r in range(2,(n-1)/2+1):
Cnr = Cnr * (n-(r-1)) / r
#print Cnr
if Cnr > MAX_EXCEED:
count += 1
count *= 2
if n%2 == 0:
Cnr = Cnr * (n/2)/(n/2+1)
if Cnr > MAX_EXCEED:
count += 1
sum += count
print sum