Probability of having two classes back to back

[Éowyn]

This isn't homework or anything but I'm trying to calculate the probability that I will have Spanish and German back to back (in either order), I've tried to solve this myself but I haven't learned this in school yet and am stuck. I have seven classes, and assuming that every possibility of class orders is equally possible, what is the probability that in any given year, I have German right after Spanish or Spanish right after German? Thanks

 

[Dr.Peterson]

This isn't homework or anything but I'm trying to calculate the probability that I will have Spanish and German back to back (in either order), I've tried to solve this myself but I haven't learned this in school yet and am stuck. I have seven classes, and assuming that every possibility of class orders is equally possible, what is the probability that in any given year, I have German right after Spanish or Spanish right after German? Thanks

There are \(7! = 7\times6\times5\times4\times3\times2\times1=5040 ways to order the 7 classes.

How many of these will involve these two classes next to one another? Give that some thought, and write back.

 

[Steven G]

You really need to define back to back? If you have Spanish, then a break and then German do you consider this back to back?
You also said what is the probability that in any given year. That is NOT very clear to me as some schools/colleges have 2 semesters/year, while others have 4 semesters/year.