## How Effective is Captcha?

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.