in a minibus there are 16 seats for passengers. How many possible seating arrangements are there for 5 passengers?

the answer in the book is 210. no idea how you get that. isn't it a simple $\displaystyle ^{16}P_5$?

furthermore in a similar question: there are 10 seats in the front row at a theatre, 6 people are shwon to this row. In how many different ways can they be seated if there are no restrictions? using $\displaystyle ^{10}P_6$ gives the textbook answer.

and there is one more question, also similar. rory has to place colored pegs into holes in a board. he has 6 identical red pegs and the board has 10 holes. how many different arrangements are there for placing the 6 pegs and leaving 4 empty holes? using $\displaystyle ^{10}P_6$ will give the textbook answer. however, these are identical pegs, not distinct people as in the previous 2 questions. using $\displaystyle ^{10}P_6$ means that arrangements such as {red peg 1, then red peg 2}, and {red peg 2, then red peg 1} are counted as 2 different arrangements. shouldn't there be more calculations involved, such as $\displaystyle ^{10}P_6 \div 6!$?