How many permutations of {1,2,3,4,5,6,7} have exactly one element fixed?
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 39RE: How many subsets does the set 1,3,5,...,99 have?
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Question
How many permutations of {1,2,3,4,5,6,7} have exactly one element fixed?
Expert Solution
Step 1
Using inclusion-exclusion principle to compute the given permutation:
There are ways to select 1 element to stay in place and permute all remaining.
But for each of ways to select 2 elements, each permutation that keeps them in place was computed 2 times, but should not be computed at all.
Thus, continuing in this manner, the desired permutation can be given by:
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