your best friend is planning a trip to the caribbean for you

your best friend is planning a trip to the caribbean for you! you will visit puerto rico, st.martin, dominican republic, turks and caicos, beliz, jamaica, u.s., virgin islands and barbados. you can visit these islands in any order except puerto rico, dominican republic and turks and caicos must be visited one after the other on the itinerary. in how many ways can your friend arrange the itinerary?

Solution

Total places to visit = 9

Total number of ways to visit these place = 9!

Now we have to visit puerto rico, dominican republic and turks and caicos in this order only

So

Now total number of visit = 9!/3! = 60480 ways.