**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, ^{5}C_{3} = 10.

In general,

^{n}C_{r} = |
n!r!(n-r)! |
,where r <= n, n! = nx(n-1)x…x3x2x1, and 0! = 1. |

It is not until `n` = 23, that a value exceeds one-million: ^{23}C_{10} = 1144066.

How many, not necessarily distinct, values of ^{n}C_{r}, for 1 <= `n` <= 100, are greater than one-million?

**Idea:**

I recognized this as another repeat of Binomial Coefficients as seen in Problem 15. I just needed to plug in the numbers in a nested loop and count how many times the answer was greater than 1 million.

int answer = 0; final BigInteger ONE_MILLION = BigInteger.valueOf(1000000); for(int n = 1; n <= 100; n++) { for(int r = 1; r <= n; r++) { if(ONE_MILLION.compareTo(EulerUtils.nChooseM(n, r)) < 0) { answer++; } } }