mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 21:41:08 +00:00
bc8df6de31
* [pre-commit.ci] pre-commit autoupdate updates: - [github.com/astral-sh/ruff-pre-commit: v0.2.2 → v0.3.2](https://github.com/astral-sh/ruff-pre-commit/compare/v0.2.2...v0.3.2) - [github.com/pre-commit/mirrors-mypy: v1.8.0 → v1.9.0](https://github.com/pre-commit/mirrors-mypy/compare/v1.8.0...v1.9.0) * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
45 lines
968 B
Python
45 lines
968 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())
|