SOLUTION: in how many different ways can 4 persons be seated in a consecutive row of seven seats?? 2. a shelf contain 5 red books, 4 blue books, and 3 green books. how many different ord

Question 716619: in how many different ways can 4 persons be seated in a consecutive row of seven seats??
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?

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
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

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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

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