Permutation with restrictions

[Guest]

Hello everybody.

I have the following problem. Three irrigation events should implemented in a 19days period. Between 2 irrigation events there should be at least a 5 days interval (i.e. if the first irrigation is implemented in day 1 the second should take place at day 6 or latter). No irrigation should be scheduled later than day 19. How can I calculate the maximum number of irrigation schedules that meet the above mentioned restrictions? I have solved the problem by hand and I know that they are 35, but is there any mathematical formula that solves the problem?

I thank is advance anyone who would spend time to read the problem and give an answer

Ioannis

[shyamjayakannan]

Since each irrigation event takes 5 days, take 3 chunks of 5 days as a group. So, the problem becomes 3 groups(5 days each) + 4 days = 19. Now, this situation is the same as finding the number of ways to arrange 3 watermelons(chunks) and 4 oranges(days) in a line, which is [tex]\frac{(3+4)!}{3!4!}=\boxed{35}[/tex].