In his landmark book An Introduction to Probability Theory and Its Applications (Wiley, 1950), William Feller describes the birthday problem, showing how to calculate the probability that in a given group of people at least two share the same month-and-day birthday. (For 23 people, this probability exceeds one-half.) Instead of talking about people sharing birthdays, one can consider words sharing letter distributions; two words having the same distribution are anagrams. It is easy to mathematically derive the probability that two or more share a birthday because the 365 possible birthdays are equally likely to occur. The analogous anagram probability is difficult to calculate because the alternatives are not equally likely (two words are far more likely to share a distribution like ARTS than ZYQQ). Instead, one must evaluate the behavior of anagrams by observation - specifically, how many of a set of W words are anagrams?
Eckler, A. Ross
"Anagrams and the Birthday Problem,"
Word Ways: Vol. 42
, Article 25.
Available at: https://digitalcommons.butler.edu/wordways/vol42/iss3/25