Family-Wise Error Rate (FWER)
The family-wise error rate is the probability of making at least one Type I error across a whole family of hypothesis tests.
If $c$ independent level-$\alpha$ tests are performed, then
$$ \text{FWER} = 1 - (1 - \alpha)^c. $$This is why naive all-pairs testing inflates the overall Type I error rate.