## Combinatoric selections

### Problem 53

Published on Friday, 26th September 2003, 06:00 pm; Solved by 36156; Difficulty rating: 5%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!(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: ^{23}C_{10} = 1144066.

How many, not necessarily distinct, values of ^{n}C_{r}, for 1 ≤ `n` ≤ 100, are greater than one-million?