From the Fun Fact files, here is a Random Fun Fact, at the Easy level: |
Suppose I return N homeworks randomly to my N students.
What is the chance that no student gets back her
own homework? In a class of 30? Would it be more or
less if I had more students?
Surprising answer: the chance that no one gets back
her own homework is approximately (1/e), which is
approximately 36.8 percent of the time!
And the answer is about the same, no matter how many
students you have! (It gets closer and closer to 1/e
the larger N gets, and is already a very good
approximation for 5 students.)
Gee, where did the number e come from?
Poll the class about the probabilities
before you tell them the answer, just to
see how good their intuition is.
The Math Behind the Fact:
This interesting fact is usually proved in classes in
discrete mathematics or probability,
using something called the inclusion-exclusion principle. The answer
turns out to be the partial sum of an infinite series
How to Cite this Page:
Su, Francis E., et al. "Matching Problem."
Math Fun Facts.
The Link for this Fun Fact:
is directly accessible here.