I am studying GCSE maths - the question I am stuck on is a probabilty question, I have answered most questions so far in the chapter when you are given the figures like 0.6, 0.5 etc however the question i am stuck on is worded differently. This is the exact wording: Each day Mr Smith runs home. He has a choice of three routes: the road, the fields or the canal path. The road route is 4 miles, the fields route is 6 miles and the canal route is 5 miles. In a three day period, what is the probability that Mr Smith runs a total distance of:

Code:

a) exactly 17 miles b) exactly 13 miles c) exactly 15 miles d) over 17 miles

Code:

the answers in the back are: a) 1/9 b) 1/9 c) 7/27 d) 1/27

I cant see how you get these answers, i have tried many different ways including tree diagrams and just listing all the possible route combinations (doing this way i get a and b correct but not c and d). A simplistic view could be that every day is an event and he has a choice of three routes, so 1/3 x 1/3 x 1/3 would seem feasable but then that would be the same for each answer, doesnt make sense. Can you please help me understand how to solve this question, I hate skipping things because I dont know them. thanks in advance