6. In this problem we consider permutation (arrangements) of the five letters A,

Question

6. In this problem we consider permutation (arrangements) of the five letters A, B, C, D, E. Suppose for any given arrangement, we are allowed to take any two adjacent letters in the sequence and reinsert them somewhere else in the sequence, without changing the order. So for example, from the sequence ABCDE we can get the sequence CABDE, CDABE, or CDEAB, by moving the adjacent pair AB. And from the sequence EDBCA we can obtain DBECA, by moving the adjacent pair DB. Using this rule repeatedly, a) Can you transform ABCDE to EDCBA? Explain. b) Can you transform ABCDE to BACDE? Explain

Explanation / Answer

6. Here we are allowed to take any two adjacent letters in the sequence ABCDE and reinsert them somewhere else in the sequence.

a) Can you transform ABCDE to EDCBA? Explain

Solution : Here we can not transform like this as, the sequence is just a reciprocal of the given sequence . No two adjacent letters are reinserted

2. Can you transform ABCDE to BACDE? Explain

Solution: This transformation also can not be done, as they didn't mention whether we are allowed to change the two adjacent letters in the sequence . (Here AB is Changed to BA)

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