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?<\/p>\n\n\n\n
Surprising answer: the chance that no one gets back her own homework is approximately (1\/e<\/em>), which is approximately 36.8 percent of the time!<\/p>\n\n\n\n And the answer is about the same, no matter how many students you have! (It gets closer and closer to 1\/e<\/em> the larger N gets, and is already a very good approximation for 5 students.)<\/p>\n\n\n\n Gee, where did the number e<\/em> come from?<\/p>\n\n\n\n Presentation Suggestions:<\/strong> The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong> How to Cite this Page:<\/strong> Fun Fact suggested by: <\/strong> Suppose I return N homeworks randomly to my N students. What is the chance that no student gets back her...<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[9,3,83,45],"class_list":["post-194","page","type-page","status-publish","hentry","tag-combinatorics","tag-easy","tag-probabilities","tag-probability"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/194","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=194"}],"version-history":[{"count":3,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/194\/revisions"}],"predecessor-version":[{"id":1522,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/194\/revisions\/1522"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=194"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=194"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Poll the class about the probabilities before you tell them the answer, just to see how good their intuition is.<\/p>\n\n\n\n
This interesting fact is usually proved in classes in discrete mathematics or\u00a0probability, using something called the inclusion-exclusion principle. The answer turns out to be the partial sum of an\u00a0infinite series\u00a0for 1\/e<\/em>.<\/p>\n\n\n\n
Su, Francis E., et al. “Matching Problem.” Math Fun Facts<\/em>. <http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n
Francis Su <\/p>\n","protected":false},"excerpt":{"rendered":"