Project Euler task 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?

----------------------------------------------------

k = 0;

For[i = 1, i <= 100, i++,

For[j = 1, j < i, j++,

If[Binomial[i, j] > 1000000,

k++

]

]

]

k