project_euler.problem_053.sol1

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! = nx(n-1)x…x3x2x1, 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?

Functions

combinations(n, r)
solution()	Returns the number of values of nCr, for 1 ≤ n ≤ 100, are greater than

Module Contents

project_euler.problem_053.sol1.combinations(n, r)

project_euler.problem_053.sol1.solution()

Returns the number of values of nCr, for 1 ≤ n ≤ 100, are greater than one-million

>>> solution()
4075