Respuesta :
Answer:
360,360
Step-by-step explanation:
This is called a Permutation with repetition, we want to know in how many ways we can arrange a certain ammount of elements (normal permutation), BUT some of those elements are identical.
The formula we use in these cases is:
[tex]\frac{n!}{n1!*n2!*...*ni!}[/tex]
where n is the total amount of elements, n1 is the amount of repeated elements of the type 1, n2 is the amount of repeated elements of the type 2, ni is the amount of repeated elements of the type i.
In this particular case we have:
[tex]n=13[/tex] (total amount of shirts)
[tex]n1=2[/tex] (small shirts)
[tex]n2=3[/tex] (medium shirts)
[tex]n3=6[/tex] (large)
[tex]n4=2[/tex] (extra large)
then the amount of orders the shirts can be sold at (arranged) is:
[tex]\frac{13!}{2!*3!*6!*2!}=360,360[/tex]
The count of orders in which the company can sell the shirts is 360360 ways.
What is the number of permutations in which n things can be arranged such that some groups are identical?
Suppose there are n items.
Suppose we have [tex]i_1, i_2, ..., i_k[/tex] sized groups of identical items.
Then the permutations of their arrangements is given as
[tex]\dfrac{n!}{i_1! \times i_2! \times ... \times i_k!}[/tex]
For the given case, there are 2 small shirts, 3 medium shirts, 6 large shirts, and 2 extra large shirts.
The seller can sell them one by one(assuming), so order of what got sold first and what got sold second matters. Seller, assuming, cannot differentiate between like sized shirts, so they are assumed identical, and thus, permutation is needed for unidentical shirts.
Total number of such orders is calculated as:
Total shirts = n = 2+3+6+2 = 13
Groups of identical items :2 small, 3 medium, 6 large, 2 extra large,
Thus, total ordering: [tex]\dfrac{n!}{i_1! \times i_2! \times ... \times i_k!} = \dfrac{13!}{2!.3!6!.2!} = 360,360[/tex]
Thus, The count of orders in which the company can sell the shirts is 360360 ways.
Learn more about permutations here:
https://brainly.com/question/13443004
