A mathematics department has 5 instructors and 12 different courses. Each instructor identifies one course as her favorite. Find the probability at least two instructors have the same favorite. Use five decimals in your answer. Solution Solving for the opposite is easier for this type of question It says find probability for at least two, But instead calculate probability of everyone having different favorite Then subtract from one. Let\'s say teacher A\'s favorite class is Class 1 Second teacher has 11/12 chance that her favorite is different Then third being also different is 10/12 Fourth and fifth would then be 9/12 and 8/12 Multiply everything and you get 0.38194 Subtract from one and you get 0.61806 chance that at least two teachers have same favorite class..