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Algebra

Blazing goIITian

Joined:	27 Dec 2010
Post:	1474

8 Feb 2012 12:05:32 IST

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257

a classic.

Mathematics

this is a very famous problem.

suppose n is a natural number.

prove that is always an integer.

if the question is not visible click on view.

or i am typing it here too(n!)!/[(n!)^(n-1)!] is an integer.

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Comments (4)

prahlad kumar sharma

Cool goIITian

Joined: 21 Jul 2010

Posts: 88

9 Feb 2012 15:25:24 IST

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suppose i have n no. of apples, n no. of oranges,n of bananas and so on such that i have (n-1)! no. of different kinds of fruits in which each kind is having n no. of fruits.

so,the total no. of fruits m having is n+n+n+n.......(upto (n-1)! terms) = n(n-1)! = n!

now if someone asks me how many arrangements of all these fruits taken all at a time is possible, then i would do this

{ since total no. of fruits is n! and there are (n-1)! different kinds of fruit and each kind contains "n " no of fruits}

And we know no. of arrangements always comes out to be an integer therefore its an integer.

sathyaram

Blazing goIITian

Joined: 25 Jul 2011

Posts: 322

9 Feb 2012 19:27:27 IST

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Wow..Superb...Nice work Prahlad :)

hemang

Blazing goIITian

Joined: 27 Dec 2010

Posts: 1474

10 Feb 2012 12:55:22 IST

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awesome method!

i didn't use the fruits though.

rest is the same...

sathyaram

Blazing goIITian

Joined: 25 Jul 2011

Posts: 322

10 Feb 2012 17:08:01 IST

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u might have used banana :p

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