Rebecca has several unbiased 12-sided dice, each with faces labeled 1 to 12. When rolling all the dice at once, the probability of rolling a 12 exactly once is equal to the probability of rolling no 12s. How many dice does Rebecca have? Let's call the number of dice n. Then the probability of rolling no 12s is 11 twelfths to the n, and the probability of rolling exactly one 12 is n times one twelfth times 11 twelfths to the n minus 1. Setting these two equal to each other, we can solve for n and find that n equals 11.

probability

12-sided dice

equal probabilities

rolling dice

solve for n