assertEquals(expected, BigIntegerMath.binomial(n, k));
      }
    }
  }

  public void testBinomialOutside() {
    for (int n = 0; n <= 50; n++) {
      try {
        BigIntegerMath.binomial(n, -1);
        fail("Expected IllegalArgumentException");
      } catch (IllegalArgumentException expected) {
      }
      try {
        BigIntegerMath.binomial(n, n + 1);

			// With 100 trials and profile fraction of 2, we expect to capture
			// 50 samples. Allow the test to pass if we get at least 20 samples;
			// the CDF of the binomial distribution says there's less than a
			// 1e-9 chance of that, which is an acceptably low flakiness rate.
			const samplingSlop = 2.5