Probability question regarding random assignment

[perfectcarrot]

Let's say there are 24 study abroad students in Europe, and they are to be placed in host homes in the U.S. in groups of 3. The assignments will be determined by a lottery system, where the names are randomly drawn to determine which of the 8 host homes the students will stay at. Let's say there are 3 siblings in that group of 24, and they are really hoping they get placed in the same home. What are the chances that this will occur?

 

[Deleted member 4993]

Let's say there are 24 study abroad students in Europe, and they are to be placed in host homes in the U.S. in groups of 3. The assignments will be determined by a lottery system, where the names are randomly drawn to determine which of the 8 host homes the students will stay at. Let's say there are 3 siblings in that group of 24, and they are really hoping they get placed in the same home. What are the chances that this will occur?

Please share your work/thoughts regarding this problem - so that we know where to begin to help you.

 

[Steven G]

P(any event) = (# of favorable outcomes)/(# of total outcomes).