1. The problem statement, all variables and given/known data Bowman shoots into a dartboard, with possible gain ranging from 0 to 10 points. Probability that he shoots 30 points in 3 shots is 0.008. Probability that he shoots < 8 in one shot is 0.4. Probability that he shoots exactly 8 in one shot is 0.15. What is the probability that he gains at least 28 points in 3 shots? 3. The attempt at a solution My solution: [tex] P(X \ge 28) = P(X = 28) + P(X = 29) + P(X = 30) [/tex] We know P(X = 30) so it's sufficient to count P(X = 28) and P(X = 29). X = 28 This situation can occur either if: (a) He shoots 10, 10 and 8 (in any order) (b) He shoots 10, 9, 9 (in any order) So I guess: [tex] (*)\ \ \ \ P(X = 28) = (P(X = 10).P(X =10).P(X = 8))+(P(X=10).P(X=9).P(X=9)) [/tex] What I'm interested in is whether this is ok. I don't know if I should take into an account that (let's take for example the case (a)) the bowman can shoot the points in any order, ie. 10, 10, 8 or 10, 8, 10 and so on. Don't I have to multiply (*) with 3! so that I cover all the orders in which the shooter can gain those points? Thank you very much.