Jun 7
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.
