in how many different ways can 4 persons be seated in a consecutive row of seven seats??
7 position 4 = P(7,4) = 7·6·5·4 = 840
----------------------------------------------------
2. a shelf contain 5 red books, 4 blue books, and 3 green books. how many different orders can they be arranged if all books of the same color must kept together?
First, there are P(3,3) = 3! ways we can choose the order of colors,
that is, (Red,Blue,Green), (Red,Green,Blue), (Blue, Red,Green),
(Blue,Green,Red), (Green,Red,Blue), (Green,Blue,Red)
Then for each of those 3! ways, there are P(5,5) = 5! ways to arrange the 5
red books, P(4,4) = 4! ways to arrange the blue books, and P(3,3) = 3! ways
to arrange the green books.
Answer 3!·5!·4!·3! = 6·120·24·6 = 103,680 ways.
Edwin
