Permutations and Combinations

Permutations and Combinations- Mental Model Series -10

“Life is full of permutations and combinations. Sometimes the order you do things matter sometimes it doesn’t, but in order to find the solution in life you must work through each possibility presented to find your opportunity.”   ― Gregory Willis, Birth of a Nephillim

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 Yes . We studied permutations and combinations in school. Though we vaguely remember about permutations and combinations  but the difference between them is bit of haze now.

Lets refresh our memory on those topics. Shall we ? .

First, the primary difference - Permutations are for lists where order matters whereas Combinations are for groups where order does not matter. Another easy hack to remember , Permutation is complicated but Combination is not.

This is not it Another one to remember well - A combination lock should really be called as "permutation lock" because a correct entry 7-9-2 is not same as 2-9-7 or 9-7-2 . The order matters.  Get it. Now let us each of these terms little closely

Permutation-

It is an arrangement of a group of objects where the order does matter.Lets consider an example of awarding Gold ,Silver and and bronze medals to a group of 8 people listed here .

A: Albert
B: Brown
C: Chris
D: Dave
E: Emma
F: Freddie
G: George
H: Haron

 since the order we hand out these medals matters, We’re going to use permutations. Here’s how it breaks down:

Gold medal: 8 choices: A B C D E F G H  Let’s say A wins the Gold.
Silver medal: 7 choices: B C D E F G H. Let’s say B wins the silver.
Bronze medal: 6 choices: C D E F G H. Let’s say… C wins the bronze.

We picked certain people to win, but the details don’t matter: we had 8 choices at first, then 7, then 6. The total number of options was 8 * 7 * 6 = 336.

Combinations :

Combination is a way of selecting some items from a collection. Like we have some items, in how many ways we can choose a few items (a fixed number) from them is called combination. For example, suppose we have three letter: a,b,c. We want to choose two letter from these three. So we can choose a,b or a,c or b,c i.e we can choose two letter in three ways. No. of ways to choose = 3. It’s the combination. In how many ways we can choose r things from a total of n things, is known as the combination and expressed as nCr. For our example 3C2 = 3.

Key Differences Between Permutation and Combination-

1. The term permutation refers to several ways of arranging a set of objects in a sequential order. Combination implies several ways of choosing items from a large pool of objects, such that their order is irrelevant.
2. The primary distinguishing point between these two mathematical concepts is order, placement, and position, i.e. in permutation characteristics mentioned above does matter, which does not matter in the case of the combination.
3. Permutation denotes several ways to arrange things, people, digits, alphabets, colours, etc. On the other hand, combination indicates different ways of selecting menu items, food, clothes, subjects, etc.
4. The permutation is nothing but an ordered combination while Combination implies unordered sets or pairing of values within specific criteria.
5. Many permutations can be derived from a single combination. Conversely, only a single combination can be obtained from a single permutation.
6. Permutation answers How many different arrangements can be created from a given set of objects? As opposed to the combination which explains How many different groups can be picked from a larger group of objects?

For more understanding  and how the formula arrived for both Permutation and combination , Please  refer to http://scaryscientist.blogspot.com/2015/03/permutations-and-combinations.html