Combinatoric Selections

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, $(\binom{5}{3}) = 10$ .

In general, $(\binom{n}{r}) = \frac{n!}{r! (n - r)!}$ , where $r \leq n$ , $n! = n \times (n - 1) \times . . . \times 3 \times 2 \times 1$ , and $0! = 1$ .

It is not until $n = 23$ , that a value exceeds one-million: $(\binom{23}{10}) = 1144066$ .

How many, not necessarily distinct, values of $(\binom{n}{r})$ for $1 \leq n \leq 100$ , are greater than one-million?

Write-up coming later

The complete problem is available here. An approach, code, and answer will be added later.