JavaScript: Calculate the combination of n and r

JavaScript Math: Exercise-42 with Solution

Calculate Combination (nCr)

Write a JavaScript function to calculate the combination of n and r.
The formula is : n!/(r!*(n - r)!).

Test Data :
console.log(combinations(6, 2));
15
console.log(combinations(5, 3));
10

Sample Solution:

JavaScript Code:

// Define a function named product_Range that calculates the product of all integers in the range [a, b].
function product_Range(a, b) {
  // Initialize the product with the value of 'a'.
  var prd = a,
      i = a;
 
  // Iterate from 'a' to 'b' (excluding 'b').
  while (i++ < b) {
    // Multiply the product by the current value of 'i'.
    prd *= i;
  }
  
  // Return the final product.
  return prd;
}

// Define a function named combinations that calculates the number of combinations (n choose r).
function combinations(n, r) {
  // Check if either 'n' equals 'r' or 'r' equals 0.
  if (n == r || r == 0) {
    // If true, return 1.
    return 1;
  } else {
    // If false, determine the larger of (n-r) and 'r' and calculate the combinations using the product_Range function.
    r = (r < n - r) ? n - r : r;
    return product_Range(r + 1, n) / product_Range(1, n - r);
  }
}

// Output the result of calculating combinations(6, 2) to the console.
console.log(combinations(6, 2));
// Output the result of calculating combinations(5, 3) to the console.
console.log(combinations(5, 3));

Output:

15
10

Flowchart:

Live Demo:

See the Pen javascript-math-exercise-42 by w3resource (@w3resource) on CodePen.

For more Practice: Solve these Related Problems:

• Write a JavaScript function that calculates nCr recursively using memoization to optimize performance.
• Write a JavaScript function that computes binomial coefficients iteratively by constructing Pascal's triangle.
• Write a JavaScript function that validates inputs for n and r, ensuring they are non-negative integers with r ≤ n.
• Write a JavaScript function that returns the combination as a formatted string, showing the calculation steps.

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