**Combinations** and **permutations** are different ways in which a group of objects can be selected and arranged into smaller subgroups. They have far-reaching, real-world applications, especially in programmatic problem-solving.  
>Python's `itertools` package provides simple functionality to compute combinations and permutations. 

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$C(n,r) = \frac{n!}{r!(n-r)!}$

$P(n,r) = \frac{n!}{(n-r)!}$
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<h2>Combinations</h2>

The `combinations` method in `itertools` takes in a list of values, alongside an integer `r`, inputs, and then returns a list of all possible combinations in the form of tuples. 
## Combinations with replacement
The `combinations_with_replacement` method works more or less the same as the simple `combinations` method, but it allows values to be combined with themselves. The following code snippet shows how these methods work:

import itertools
 
vals = [16, 12, 24, 73, 2, 24]
 
comb = itertools.combinations(vals, 3)

comb_with_rep = itertools.combinations_with_replacement(vals, 3)

print("Combinations without replacement:")
for val in comb:
    print(*val)

print("Combinations with replacement:")
for val in comb_with_rep:
    print(*val)

<h2>Permutations</h2>

The `itertools` package provides a similar functionality to compute permutations. The `permutations` method takes a list as input and an optional integer (`r`) that defines the length of the desired permutations. The code below shows how permutations can be computed in Python:

import itertools
 
vals = [16, 12, 24, 73]
 
perm = itertools.permutations(vals)

perm_r = itertools.permutations(vals, 2)

print("Permutations of length 4:") # Same length as list vals
for val in perm:
    print(*val)

print("Permutations of length 2:")
for val in perm_r:
    print(*val)

Combinations and permutations in Python

Python's itertools provides functions to compute combinations and permutations, useful for problem-solving.