Concept explainers
(a)
The value of the permutations
(a)
Answer to Problem 1E
The permutations
Explanation of Solution
The given permutations are,
Here,
Thus,
Similarly,
Thus,
Therefore, the permutations are
(b)
The value of the permutation
(b)
Answer to Problem 1E
The permutations
Explanation of Solution
The given permutations are,
Obtain the permutation
Interchange the rows of the permutation f.
Then, the permutation will be
Arrange the columns of the permutation
Thus,
Obtain the permutation
Interchange the rows of the permutation g.
Then, the permutation will be
Arrange the columns of the permutation
Thus,
Therefore, the permutations are
(c)
The values of the permutation
(c)
Answer to Problem 1E
The permutations are
Explanation of Solution
The given permutation is,
Obtain the permutation
Here,
Clearly,
Therefore,
That is,
Obtain the permutation
Here,
Clearly,
Thus,
Now, compute
Clearly,
Thus,
Therefore, the permutations are
(d)
The value of the permutation
(d)
Answer to Problem 1E
The permutations is
Explanation of Solution
The given permutations are,
Obtain the permutation
From part (a),
Clearly,
Thus,
Therefore, the permutations is
(e)
The value of the permutation
(e)
Answer to Problem 1E
The permutations are
Explanation of Solution
The given permutations are,
Obtain the permutation
Here,
Clearly,
Thus,
Similarly,
Thus,
From part (b), the permutation
Now, obtain the permutation
Clearly,
Thus,
Similarly,
Thus,
Therefore, the permutations are
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Chapter 14 Solutions
Introductory Combinatorics
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