Solution: Use inclusion-exclusion. Total assignments: $3^6 = 729$. Subtract assignments missing at least one category: $3 \times 2^6 = 192$. Add back assignments missing two categories: $3 \times 1^6 = 3$. Valid assignments: $729 - 192 + 3 = 540$. \boxed540Question: An electrical engineer tests a new circuit with 5 identical resistors, each with a 10% probability of failing independently. What is the probability that exactly 2 resistors fail? - Groen Casting