Captcha is a method to reduce spam on the internet. Spambots crawl thew internet looking for ways to post links. If they can register for a website, they can often post links. One type of captcha makes users select pictures of a certain type. The captcha below contains nine pictures.
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The users is expected to select the three pictures containing signs with street names. There are
\[{}^9 C_3 = \frac{9!}{3! (9-3)!} ==84\]
ways of doing this, so the probability of randomly picking the 3 correct pictures is
\[\frac{1}{84}\]
.
This means that a spambot will guess wrong
\[\frac{83}{84} \times 100 \% - 98.8 \%\]
of the time.