This website is a semi-functional mirror of the original Project Euler. More information is available on GitHub.
projecteuler.net

Combinatoric selections

Problem 53

Published on 26 September 2003 at 06:00 pm [Server Time]

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?


Answer:
Go to back to Problems