22) A fair die with faces numbered from 1 to 6 is rolled three times, and each time a stick of length equal to the result of the roll is taken. What is the probability that the three sticks form the sides of a right triangle?
(A) $\frac{1}{6}$
(B) $\frac{1}{36}$
(C) $\frac{1}{216}$
(D) $\frac{5}{18}$
(E) $\frac{1}{72}$.
22) The answer is (B)

The only right-angled triangle that can be constructed with sides of integer length between 1 and 6 has sides of length 3, 4, and 5. The probability that the rolls produce the three results 3, 4, and 5 is: $\frac{3}{6}$ (probability that the first roll gives one of the three results), multiplied by $\frac{2}{6}$ (probability that the second roll gives one of the other two results), multiplied by $\frac{1}{6}$ (probability that the third roll gives the last result). In total, the probability is therefore $\frac{3}{6} \times \frac{2}{6} \times \frac{1}{6}=\frac{1}{36}$.