11 lines
473 B
Markdown
11 lines
473 B
Markdown
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, `C(5,3) = 10`.
|
|
|
|
In general, `C(n,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: `C(23,10) = 1144066`.
|
|
|
|
How many, not necessarily distinct, values of `C(n,r)`, for `1 <= n <= 100`, are greater than one-million? |