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# Problem 53

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, 5C3 = 10.

In general,

nCr=$\frac{n!}{r!(n-r)!}$, 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: 23C10 = 1144066.

How many, not necessarily distinct, values of  nCr, for 1 ≤ n ≤ 100, are greater than one-million?

123、124、125、134、135、145、234、235、245和345

nCr=$\frac{n!}{r!(n-r)!}$，其中r ≤ n，n! = n×(n−1)×…×3×2×1，且0! = 1。