Combinatoric selections
Problem 53
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, .
In general, , where , , and .
It is not until , that a value exceeds one-million: .
How many, not necessarily distinct, values of for , are greater than one-million?
def run():
total = 0
n = 23
r = 10
value = 1144066
while n <= 100:
while value > 1e6:
r -= 1
prev = value
value = value * (r + 1) / (n - r)
value = prev
r += 1
total += (n - r) - r + 1 # e.g. 23C10 ... 23C13
n += 1
value = value * n / (n - r)
return total