Final answer:
To find the number of different schedules possible for Osas, we use the principle of counting and consider different cases. The total number of schedules is 2380.
Step-by-step explanation:
To find the number of different schedules possible for Osas, we need to consider the restrictions given. He can choose between swimming, fishing, or land-based sports each day, but he cannot do different water sports on consecutive days. Additionally, he wants to try all three options on at least one day of his holiday.
Let's use the principle of counting to solve this problem:
- First, consider that Osas has 8 days to plan his activities.
- Next, choose one day on which Osas will try all three options (swimming, fishing, and a land-based sport). This can be done in one way.
- Now, we can divide the remaining 7 days into two cases: Case 1 where all 7 days have the same activity, and Case 2 where the activities are split.
- In Case 1, Osas can choose any one of the three options for each of the 7 days. This can be done in 37 ways.
- In Case 2, Osas can choose any one of the three options for the first day, any one of the two remaining options for the second day, and so on, until the 7th day. This can be done in 3 * 2 * 2 * 2 * 2 * 2 * 2 = 3 * 26 ways.
Finally, summing up the total number of possibilities, we get:
Total number of schedules = 1 + 37 + 3 * 26 = 1 + 2187 + 192 = 2380.