Question

Kevin has four red marbles and eight blue marbles. He arranges these twelve marbles randomly, in a ring. How do you determine the probability that no two red marbles are adjacent?

Answer 1

Answer:

I came up with 7/33 ~ 21.2%

The total number of possible ball combinations where 4 are red and 8 are blue is:

12!/(8! * 4!) = 495

The number of combinations where red doesn't repeat is 105.  

I'm sure there's a formula for this, but I just counted out each scenario. For example, if marble 1 is red, there are 35 ways to have 3 more red marbles that aren't consecutive. The same is true for marble 2 being red. Then for marble 3 being red, there are 20 ways without having consecutive red marbles or a red marble 1. Etc...you eventually end up with:

35+35+20+10+4+1=105

So that makes the probability that no two red marbles are adjacent:

105/495 = 7/33

Step-by-step explanation: