Project Euler Problem 53 Statement
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?
Solution
HackerRank version
How many, not necessarily distinct, values of 5C3, for 1 ≤ n &le N, are greater than K?
Python Source Code
import math
N, K = map(int,input().split())
c = 0
for n in range(2, N+1):
for r in range(2, n//2):
if math.comb(n, r) > K:
c+= (n + 1 - 2*r)
break
print(c)