# Python – math.comb() method

Math module in Python contains a number of mathematical operations, which can be performed with ease using the module. `math.comb()` method in Python is used to get the number of ways to choose k items from n items without repetition and without order. It basically evaluates to n! / (k! * (n – k)!) when k n. It is also known as binomial coefficient because it is equivalent to the coefficient of k-th term in polynomial expansion of the expression (1 + x)n.
This method is new in Python version 3.8.

Syntax: math.comb(n, k)

Parameters:
n: A non-negative integer
k: A non-negative integer

Returns: an integer value which represents the number of ways to choose k items from n items without repetition and without order.

Code #1: Use of `math.comb()` method

 `# Python Program to explain math.comb() method ` ` `  `# Importing math module ` `import` `math ` ` `  `n ``=` `10` `k ``=` `2` ` `  `# Get the number of ways to choose ` `# k items from n items without ` `# repetition and without order ` `nCk ``=` `math.comb(n, k) ` `print``(nCk) ` ` `  `n ``=` `5` `k ``=` `3` ` `  `# Get the number of ways to choose ` `# k items from n items without ` `# repetition and without order ` `nCk ``=` `math.comb(n, k) ` `print``(nCk) `

Output:

```45
10
```

Code #2: When k > n

 `# Python Program to explain math.comb() method ` ` `  `# Importing math module ` `import` `math ` ` `  `# When k > n  ` `# math.comb(n, k) returns 0. ` `n ``=` `3` `k ``=` `5` ` `  `# Get the number of ways to choose ` `# k items from n items without ` `# repetition and without order ` `nCk ``=` `math.comb(n, k) ` `print``(nCk) `

Output:

```0
```

Code #3: Use of `math.comb()` method to find coefficient of k-th term in binomial expansion of expression (1 + x)n

 `# Python Program to explain math.comb() method ` ` `  `# Importing math module ` `import` `math ` ` `  `n ``=` `5` `k ``=` `2` ` `  `# Find the coefficient of k-th ` `# term in the expansion of  ` `# expression (1 + x)^n ` `nCk ``=` `math.comb(n, k) ` `print``(nCk) ` ` `  `n ``=` `8` `k ``=` `3` ` `  `# Find the coefficient of k-th ` `# term in the expansion of  ` `# expression (1 + x)^n ` `nCk ``=` `math.comb(n, k) ` `print``(nCk) `

Output:

```10
56
```

Reference: Python math library

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