# Permutation

A mathematical technique used when the order of a set matters.

When the order of the arrangements counts, a permutation is a mathematical approach that specifies the number of alternative arrangements in a collection. A common mathematics problem involves selecting only a few items from a group of objects in a specific sequence.

Permutations are commonly mistaken with combinations, another mathematical approach. In **combinations**, however, the order of the various components has no effect on the selection. In other words, the configurations ABand BEin permutations are regarded separate arrangements, but they are **equivalent** in combinations.

The generic permutation formula is written as follows:

where:

n -> the total number of elements in a set.

k -> the number of items chosen and placed in a given sequence

! -> factorial

**Factorial (**noted as “!”) is the product of all positive integers less than or equal to the number preceding the factorial sign. For example, 3! = 1 x 2 x 3 = 6.

The formula above is utilized when we wish to choose only a few elements from a group of elements and **arrange them** in a certain order.

*Example of a Permutation:*

You work at a private equity firm. You intend to put $5 million into two initiatives. Instead of allocating funds evenly, you opted to spend $3 million in the most promising project and $2 million in the least potential initiative.** Six initiatives** were identified by your experts for prospective investment. How many **different options** are there for your investing decision?

This example is a **permutation issue**. Because the funds allocated to the two projects are not equal, the order of selection is important in this scenario. Take a look at the following arrangement:

Invest** $3 million in Project A and $2 million in Project B** as opposed to investing** $2 million in Project A and $3 million in Project B.**

The alternatives are **not equivalent**. As a result, we must apply the following formula to find the number of possible arrangements:

As a result, depending on the **six ideas** chosen by your experts, you may generate **30 potential investment arrangements**.