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# There are 4 copies of 5 different books. In how many ways

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Director
Joined: 30 Nov 2006
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Location: Kuwait
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There are 4 copies of 5 different books. In how many ways [#permalink]  04 May 2007, 15:00
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There are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?

A) 20!/4!

B) 20!/5(4!)

C) 20!/(4!)^5

D) 20!

E) 5!
VP
Joined: 08 Jun 2005
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we know that there are 5 different topics contining 4 copies (same book) each.

Total ways to arrange all books (we will ignore the fact that there are copies). = 20!

we know that 4 books are the same so we will have to "remove" repetition from 20!

4! (removing set one) * 4! (removing set two) * 4! (removing set three) * 4! (removing set four) * 4! (removing set five).

hence: 20!/4!*4!*4!*4!*4! = 20!/4!^5

to better understand lets think about 3 balls - 2 red (R1&R2) and 1 blue (B1). the total ways to arrange the balls is 3! = 6

R1R2B1
R1B1R2
R2B1R1
R2R1B1
B1R1R2
B1R2R1

but now we want to remove all the places that R1R2=R2R1 becuase that is the same thing !! (replacing red and red is the same).

since we have 2 reds in one repeating set (reds) we will remove repetition in 2!

so the outcome is 3!/2! = 3 , try to remove from the table above all the places that R1R2=R2R1 and you will get 3.

Director
Joined: 14 Jan 2007
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Mine is 'C' too. Good explanation by Killer...
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# There are 4 copies of 5 different books. In how many ways

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