Respuesta :
Answer:
The total number of different arrangements is 560.
Step-by-step explanation:
A multiset is a collection of objects, just like a set, but can contain an object more than once.
The multiplicity of a particular type of object is the number of times objects of that type appear in a multiset.
Permutations of Multisets Theorem.
The number of ordered n-tuples (or permutations with repetition) on a collection or multiset of [tex]n[/tex] objects, where there are [tex]k[/tex] kinds of objects and object kind 1 occurs with multiplicity [tex]n_1[/tex], object kind 2 occurs with multiplicity [tex]n_2[/tex], ... , and object kind [tex]k[/tex] occurs with multiplicity [tex]n_k[/tex] is:
[tex]\begin{equation*}\frac{n!}{n_1!*n_2!*\dots * n_k!}\end{equation*}[/tex]
We know that a boy has 3 red, 2 yellow and 3 green marbles. In this case we have n = 8.
If marbles of the same color are indistinguishable, then the total number of different arrangements is
[tex]{8 \choose 3, 2, 3} = \frac{8 !}{3 ! 2 ! 3 !} = \frac{8\cdot \:7\cdot \:6\cdot \:5\cdot \:4}{2!\cdot \:3!}=\frac{6720}{2!\cdot \:3!}=\frac{6720}{12}=560[/tex]
