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Algebra

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10 Feb 2012 07:35:05 IST

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Permutations

Mathematics

If A denotes the no. Of permutations of ( x + 2 ) things taken all at a time , B denotes the no. of permutations of ( x ) things taken 11 at a time and C the no. Of permutations of ( x - 11 ) things taken all at a time such that A = 182 BC, find the value of x.

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Aashish jaiswal

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Joined: 9 Feb 2012

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10 Feb 2012 10:44:43 IST

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hemang

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10 Feb 2012 13:01:15 IST

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there is a bigmistake in the problem. you didn't mention if the things were distinct or not. ;)

assuiming they are distinct (cause it is the only case the problem cn be solved given the conditions).

we have A = (x+2)!.

B = (x!)(x-11)!

C = (x-11)!

using the relation given we get -

(x+2)! = 182 (x!).

or, (x+1)(x+2) = 182.

or, x^2 + 3x + 2 = 182.

or x^2 + 3x - 180 = 0.

x^2 + 15x - 12x - 180 = 0.

(x+15)(x-12) = 0.

since x is a natural number, x = 12.

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