Suppose the final result of a football match is 5−4, the home team winning. If the home team scored first and kept the lead until the end, in how many different orders could the goals have been scored?
I have seen this problem at many places but I don't know how to solve this problem. The latest I have seen this in a facebook group. The answer given is 9. I am not sure if it's the correct answer. Can anyone explain how to solve it except for writing all the possible cases.
2026-04-11 15:50:25.1775922625
A common combinatorics problem
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1
You could easily try to find the general solution by plotting a lattice path where the horizontal denotes the current score of the home team and the vertical denotes the current score of the visiting team.
Looking at this way for your case, we can easily see that the number of possibilities reflects that of the 4th Catalan number which is 14. You can see the 14 possibilities in of the examples listed: http://en.wikipedia.org/wiki/Catalan_number#Applications_in_combinatorics