1. The problem statement, all variables and given/known data A quadratic eqn of form ax2 + bx + c = 0 is selected. The values of a, b and c are distinct and selected from 1, 2, 3, 4, 6, 8, 9. What is probability of chosen equation to have equal roots? 2. Relevant equations root = (-b +/- Sqrt(b2-4ac)) / (2a) For equal roots b2 = 4ac 3. The attempt at a solution well i found out that for b2 = 4ac, the conditions are b=6, a = 1, c = 9. b=6, a = 9, c = 1. Probability = no. of likely events/total no. of events. Probability of A and B to occur = P(A)*P(B) Case 1--- So probability of value of a to be 6 is 1/7. (as total 7 numbers are there) Probability of value of b to be 1 is 1/7 Probability of c to be 9 is 1/7. Case 2--- Likewise Probability of a to be 6 is again 1/7 P(b=9) = 1/7 P(c=1) = 1/7 P(equal roots) = P(case 1) + P(case 2) = 1/73 + 1/73 =2/343 But in solutions it goes like: there are two ways in which condition can be achieved for equal roots. Total ways = 7P3. So P(equal roots) = 2/(7P3) Why is my method wrong? And why should it be 7P3 and not 7C3?