Answer:
3150 different ways to rearrange the marbles.
Step-by-step explanation:
This is a very simple combinatoric. The formula for a situation in which we are looking to find the distinct ways of arrangement for three different objects is:
[tex]\frac{n!}{a*b*c}[/tex]
where n represents the total number of objects to rearrange.
a,b,c represents the the total ways to move around the their corresponding type of object in a similiar fashion. (i.e., a = (# of pink marbles)!, b = (# blue marbles)!, c = (# of orange marbles)!).
Since there is always a x! amount of ways to rearrange a collection of similiar order, we can account for the overcounting via taking the factorial of each of the different quantities.
Thus, we get
[tex]\frac{10!}{2!*4!*4!} = 3150[/tex]
