Mudd Math Fun Facts!
hosted by the Harvey Mudd College Math Department created, authored and ©1999-2007 by Francis Su
You can now subscribe to our RSS feed to get the latest Fun Facts!
Get a random Fun Fact!
No subject limitations
Search only in selected subjects
    Algebra
    Calculus or Analysis
    Combinatorics
    Geometry
    Number Theory
    Probability
    Topology
    Other subjects
  Select Difficulty  
Enter keywords 

  List All : List Recent : List Popular
  About Math Fun Facts / How to Use
  Contributors / Fun Facts Home
© 1999-2007 by Francis Edward Su
All rights reserved.

From the Fun Fact files, here is a Fun Fact at the Easy level:

Matching Problem

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?

Presentation Suggestions:
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 for 1/e.

How to Cite this Page:
Su, Francis E., et al. "Matching Problem." Mudd Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

Bookmark this page on: | Digg this! | Del.icio.us | Technorati | Reddit | Fark | Squidoo | Furl | Blinklist | Yahoo MyWeb | Google | Stumbleupon |

Keywords:    probability, combinatorics
Subjects:    combinatorics, probability
Level:    Easy
Fun Fact suggested by:   Francis Su
Suggestions? Use this form.
3.26
 
current
rating 		Click to rate this Fun Fact...
    *   Awesome! I totally dig it!
    *   Fun enough to tell a friend!
    *   Mildly interesting
    *   Not really noteworthy
and see the most popular Facts!

Want another Math Fun Fact?

For more fun, tour the Mathematics Department at Harvey Mudd College!