Question

2.4 statistics A clothing store has a certain shirt in 4 sizes: small, medium, large, and extra large. If it has 2 small, 3 medium, 6 large, and 2 extra large in stock, in how many orders can it sell all the shirts?

Answer 1

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:

$\frac{n!}{n1!*n2!*...*ni!}$

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:

$n=13$ (total amount of shirts)

$n1=2$ (small shirts)

$n2=3$ (medium shirts)

$n3=6$ (large)

$n4=2$ (extra large)

then the amount of orders the shirts can be sold at (arranged) is:

$\frac{13!}{2!*3!*6!*2!}=360,360$