# What is Combinations and Permutations?

Today, I will discuss with you what is the concept of **Combinations* and *Permutations*, and how to use them in programming.

I will be using Python to apply these concepts in programming, but language doesn't matter here, the concept is what matters, so whatever language you decide to use, there will be a library which gives you access to combinations and permutations.

In Python, **itertools** is the library that I use for combinations and permutations.

```
import itertools
```

### Here is the main header in this article:

- What is Combinations and Permutations
- Apply Combinations and Permutations using Python
- Real Problems for Combinations and Permutations

### What is Combinations and Permutations

Both of **Combinations** and **Permutatinos** are mathematical concepts, and they are for finding all different/possible ways in which you can group list of items, but they differ in the order of items for each group:

- In combinations the order
**does not**matter. - In permutations the order
**does**matter.

### Apply Combinations and Permutations using Python

The methods `combinations`

and `permutations`

of `itertools`

library receive two parameters, one is for interable object (e.g list), the second is how many items to include in each group.

#### Combinations Example:

We are looking for all different groups of **3** items from **my_list**.

```
my_list = [1, 2, 3]
combinations = itertools.combinations(my_list, 3)
for c in combinations:
print(c)
```

```
(1, 2, 3)
```

Since the order doesn't matter, and **my_list** is a list of size 3, then we can only get one group.

So what about finding the different groups of **2** items?

```
my_list = [1, 2, 3]
combinations = itertools.combinations(my_list, 2)
for c in combinations:
print(c)
```

```
(1, 2)
(1, 3)
(2, 3)
```

Now we get more one group of **2** items, definitely they are more if the order matters, we will see it in `permutations`

example.

#### Permutations Example:

Let's see all different groups of **2** items from **my_list**.

```
my_list = [1, 2, 3]
permutations = itertools.permutations(my_list, 2)
for p in permutations:
print(p)
```

```
(1, 2)
(1, 3)
(2, 1)
(2, 3)
(3, 1)
(3, 2)
```

See? since order does matter in Permutations, `(1, 2)`

will be different group than `(2, 1)`

, and we will get more groups than Combinations method.

### Real Problems for Combinations and Permutations

So, let's see some real problems to learn how this might be important.

**Problem**:

Given list of positive numbers, print list of possible groups of 3 numbers so the sum of numbers in the same group equals 10.

**Solution**:

In this problem, order won't matter because both `1 + 3 + 6`

and `3 + 1 + 6`

will equal 10, so Combinations fits this problem.

```
my_list = [1, 2, 3, 4, 5, 6]
combinations = itertools.combinations(my_list, 3)
print( [result for result in combinations if sum(result) == 10] )
```

```
[(1, 3, 6), (1, 4, 5), (2, 3, 5)]
```

**Problem**:

Given a string of random letters, check if there is a group of these letters matches the word 'sample'.

**Solution**:

Order does matter here because `as`

doesn't equal to `sa`

, so Permutations fits this problem.

```
word = 'sample'
string = 'plmeas'
permutations = itertools.permutations(string, len(string))
for p in permutations:
if ''.join(p) == word:
print('Match!')
break
else:
print('No Match!')
```

```
Match!
```

That's all for today article, hope you like it.

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