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Question

The maximum number of permutations of 2n letters in which there are only a′s and b′s. taken all at a time is given by :

A
2nCn
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B
21.62.103....4n6n1.4n2n
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C
n+11.n+22.n+33n+44.....2n1n1.2nn
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D
2n[1.3.5....(2n3)(2n1)]n!
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Solution

The correct option is A 2nCn
Given 2n letters
Are in the form of a & b.
Let us suppose that x as we have
Then we will have 2nx bs
i.e, 2n!x!(2nx)!=2nCx [nCx=n!x!(nx)!]
2nCx is maximum when x is half of 2n
i.e; x=2n2=n
so we can write 2nCx=2nCn

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