Respuesta :
We will investigate the counting principles that are used for cases of probability evaluation.
There are two possible types of counting principles.
Combinations:
It gives us the total number of possible selections that you can make "given" - " for " something. It is a simple selection process between the subejct and an object. The notation used for determining the number of selections/combinations is expressed as:
[tex]^nC_r[/tex]Where,
[tex]\begin{gathered} n\colon\text{ Total number of subjects} \\ r\colon\text{ Total number of ob}\imaginaryJ ects \end{gathered}[/tex]Then we can use the calculator infused functions of " C " combinatorics!
Permutations:
It gives us the total number of possible arrangements comprised of selections and shuffling that you can make "given" - " for " something. It is a simple selection and shuffling process of subject and object. The notation used for determining the number of selections/combinations and re-shuffling is expressed as:
[tex]^nC_r\cdot\text{ r!}[/tex]The above means that to determine arrangements we first need to find the number of combinations " C " between the subject and object then we will re-shhuffle the order of each combination paired with an object!
We are given the following:
[tex]\begin{gathered} \text{Subject : people} \\ \text{Object : chairs} \end{gathered}[/tex]The corresponding variables are:
[tex]\begin{gathered} n\text{ = 25} \\ r\text{ = 15} \end{gathered}[/tex]We are to determine the total number of possible arrangements that are possible. Hence, we are looking at the case of permutations that involves the selection and re-shuffle process.
The total number of arrangements can be made as such:
[tex]\begin{gathered} ^{25}C_{15}\cdot15! \\ 4.27\cdot10^{18}\text{ possible arrangements} \end{gathered}[/tex]
