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# If there are 4 pictures of different sizes, in how many ways

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Senior Manager
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If there are 4 pictures of different sizes, in how many ways [#permalink]

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16 May 2004, 11:46
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If there are 4 pictures of different sizes, in how many ways there are at least one small picture between the large 2 pictures?

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Manager
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16 May 2004, 11:54
hallelujah1234 wrote:
If there are 4 pictures of different sizes, in how many ways there are at least one small picture between the large 2 pictures?

2 is between 1 and 3.

n pictures, 3 pictures should be in some order.

2*n!/3! pictures, because we have n!/3! ways to arrange all books if 1 is before 3, and the same n!/3! ways to arrange all books if 3 is before 1.

8 ways?

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Senior Manager
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18 May 2004, 12:44
hallelujah1234 wrote:
If there are 4 pictures of different sizes, in how many ways there are at least one small picture between the large 2 pictures?

a b c d

let a b c as one group where b & d are the small picture

the group & d makes comb 2!
b & d can interexchange position in comb 2!
a & c can interexchange position in comb 2!

so it is 2!*2!*2!=8

Last edited by mirhaque on 18 May 2004, 12:50, edited 1 time in total.

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18 May 2004, 12:48
( total arrangements ) - ( arrangements in which 2 big ones are together )

4!-2*3! = 24-12 = 12 ways.

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18 May 2004, 12:51
anandnk wrote:
( total arrangements ) - ( arrangements in which 2 big ones are together )

4!-2*3! = 24-12 = 12 ways.

i see your logic. you r right. can you pls point out flaws with my prior post's logic?

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18 May 2004, 12:51
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