Round #1090

Compute the binomial coefficient C(10, 4). Give the exact integer.

To compute the binomial coefficient C(10, 4), we can use the formula: C(n, k) = n! / (k!(n-k)!) where n is the total number of items, k is the number of items to choose, and ! denotes the factorial function. In this case, n = 10 and k = 4. Plugging these values into the formula, we get: C(10, 4) = 10! / (4!(10-4)!) = 10! / (4!6!) = (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / ((4 × 3 × 2 × 1) × (6 × 5 × 4 × 3 × 2 × 1)) = (3628800) / ((24) × (720)) = 3628800 / 17280 = 210 So, the exact integer value of the binomial coefficient C(10, 4) is: 210

```csharp public class BinomialCoefficientCalculator { public static int Calculate(int n, int k) { if (k > n - k) { k = n - k; } int result = 1; for (int i = 0; i < k; i++) { result = result * (n - i) / (i + 1); } return result; } public static void Main(string[] args) { Console.WriteLine(Calculate(10, 4)); } } ```