(a) A palindrome is a string whose reversal is identical to the string. How many
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Question
(a) A palindrome is a string whose reversal is identical to the string. How many bit strings of length n are palindromes? (b) In how many ways can a photographer at a wedding arrange seven people in a row, including the bride and groom, if (i) the bride must be next to the groom. (ii) the bride is not next to the groom. (iii) the bride is positioned somewhere to the left of groom. (a) Five men and three women need to sit down for dinner at a circular table. (i) In how many ways can this be done? (ii) In how many ways can this be done if no two women may sit next to each other? A 9-member computer science department must select one person to chair the distance mathematics committee and two other people to co-chair the theory of computation committee. (i) In how many ways can this be done? (ii) In how many ways can this be done if Professor Olson refuses to chair the discrete mathematics committee? (iii) In how many ways can this be done if Professor Martin refuses to chair the theory of computation committee?Explanation / Answer
A) how many bit strings of lenghth n are palindrome ?
2(n+1)/2 if n is odd and 2n/2 if n is even
supoose we have 3 bits , Number of palindromes are : {000, 111, 010, 101} = 4 [ 2(n+1)/2 ]
supoose we have 2 bits , Number of palindromes are : {00, 11} = 2 [ 2n/2 ]
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