Some math related code for calculatin binomial coef, nth-fibonacci and sin

bincoef.c

@@ -0,0 +1,38 @@
+#include <stdio.h>
+
+/**
+ * @brief Computes the binomial coefficient "n choose k" (nCk).
+ *
+ * This function calculates the number of ways to choose k elements from a set
+ * of n elements without repetition and without order. It uses an efficient
+ * multiplicative approach to avoid large intermediate factorials.
+ *
+ * @param n The total number of elements.
+ * @param k The number of elements to choose.
+ * @return The computed binomial coefficient (n choose k), or 0 if k > n.
+ */
+unsigned long long binomial_coefficient(unsigned int n, unsigned int k);
+
+unsigned long long binomial_coefficient(unsigned int n, unsigned int k) {
+    if (k > n)
+        return 0;
+    if (k == 0 || k == n)
+        return 1;
+
+    if (k > n - k)
+        k = n - k;
+
+    unsigned long long result = 1;
+    for (unsigned int i = 1; i <= k; ++i) {
+        result *= n - (k - i);
+        result /= i;
+    }
+
+    return result;
+}
+
+int main() {
+    unsigned int n = 10, k = 3;
+    printf("C(%u, %u) = %llu\n", n, k, binomial_coefficient(n, k));
+    return 0;
+}