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, ^{5}C_{3} = 10.
In general,
^{n}C_{r} = |
n! r!(nr)! |
,where r n, n! = n(n1)...321, and 0! = 1. |
It is not until n = 23, that a value exceeds one-million: ^{23}C_{10} = 1144066.
How many, not necessarily distinct, values of ^{n}C_{r}, for 1 n 100, are greater than one-million?
These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK