Permutations

Question

Comments

is it D?

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C is correct. @skyby you even need to consider the case of odd palindrome also.

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but in case of odd length we don't care what's the middle element should be as it will be palindrome if it changes too so why we count it?

Answer 1

let consider the

case1:- n is even

then we will focus on the permutation n/2 bits and remaining n/2 will arrange in one way...i.e 2^n/2

case2;- n is not even 

then we will calculate the permutation of n-1/2 bits ...and remaining n-1/2 bits could arrange in one way..

middle bits could be 0 or 1  ,...therefor total number of palindrome with n-odd would be 2 ^{n-1 /2}  *2 => 2 ^{((n-1) /2) +1} 

=>2 ^n+1 /2 or we can write it as  2 ^ceil(n/2)