473 B
473 B
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?