Combinatoric selections

There are exactly ten ways of selecting three from five, \( 12345 \):

\[ 123, 124, 125, 134, 135, 145, 234, 235, 245,\text{ and }345 \]

In combinatorics, we use the notation, \( \displaystyle \binom 5 3 = 10 \).

In general, \( \displaystyle \binom n r = \dfrac{n!}{r!(n-r)!} \), where \( r \le n \), \( n!=n \times (n-1) \times ... \times 3 \times 2 \times 1 \), and \( 0!=1 \).

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

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