Euler problem 53

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 =

n! r!(nr)!

,where r  n, n! = n(n1)...321, and 0! = 1.

It is not until n = 23, that a value exceeds one-million: ²³C₁₀ = 1144066.

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

 performance improvements:

 1) add break:               12374 us -> 880 us
 2) let minimun n=23, r=4: 880 us -> 277 uS



Problem 53 =        4075 elapsed time:    0 ms. Test Passed.