mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 13:49:30 +00:00
44254cf112
* Rename all Project Euler directories: Reason: The change was done to maintain consistency throughout the directory and to keep all directories in sorted order. Due to the above change, some config files had to be modified: 'problem_22` -> `problem_022` * Update scripts to pad zeroes in PE directories
44 lines
967 B
Python
44 lines
967 B
Python
"""
|
||
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, 5C3 = 10.
|
||
|
||
In general,
|
||
|
||
nCr = n!/(r!(n−r)!),where r ≤ n, n! = n×(n−1)×...×3×2×1, 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?
|
||
"""
|
||
from math import factorial
|
||
|
||
|
||
def combinations(n, r):
|
||
return factorial(n) / (factorial(r) * factorial(n - r))
|
||
|
||
|
||
def solution():
|
||
"""Returns the number of values of nCr, for 1 ≤ n ≤ 100, are greater than
|
||
one-million
|
||
|
||
>>> solution()
|
||
4075
|
||
"""
|
||
total = 0
|
||
|
||
for i in range(1, 101):
|
||
for j in range(1, i + 1):
|
||
if combinations(i, j) > 1e6:
|
||
total += 1
|
||
return total
|
||
|
||
|
||
if __name__ == "__main__":
|
||
print(solution())
|