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The following is how Niloy can go to the office from home:  

Home → (Four Roads) → Schools → (Three Roads) → University → (Five Roads) → Parks → (Two Roads) → Offices  

Niloy is forgetful minded. He may have forgotten something at home. He remembers what he forgot at home, either at his school or university or in the park, and he goes back to pick it up. Then the journey continues from the beginning again. Niloy forgets one thing at most during the day and when he reaches the office he does not go back to take back what he has left. So how many different roads is possible for him?


Combinatorics  


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Attempt 426


Solve 198


First Solve Mesbatur_Rahman_Niloy