Counting Permutations A permutation of the set [10] = {1,2, 3, ., 10} is a way of listing the elements of (10] in order so that each element appears eractly once. The following questions ask about counting the number of permutations of [10] with certain properties. Remember to justify your %3D answers. (d) How many permutations of [10] start with k, k – 1, k – 2, ., 1 for some integer k? (e) How many permutations of [10] have 1 appear earlier in the sequence than 10? (f) How many permutations of [10] have all of the even numbers appearing in the first seven positions?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A permutation of the set [10] = {1, 2, 3, ..., 10} is a way
of listing the elements of [10] in order so that each element appears exactly once. The following questions
ask about counting the number of permutations of [10] with certain properties. Remember to justify your
Counting Permutations
answers.
(d) How many permutations of [10] start with k, k – 1, k – 2, .., 1 for some integer k?
(e) How many permutations of (10] have 1 appear earlier in the sequence than 10?
(f) How many permutations of [10] have all of the even numbers appearing in the first seven positions?
(9) How many permutations of (10] alternate even and odd numbers?
Transcribed Image Text:A permutation of the set [10] = {1, 2, 3, ..., 10} is a way of listing the elements of [10] in order so that each element appears exactly once. The following questions ask about counting the number of permutations of [10] with certain properties. Remember to justify your Counting Permutations answers. (d) How many permutations of [10] start with k, k – 1, k – 2, .., 1 for some integer k? (e) How many permutations of (10] have 1 appear earlier in the sequence than 10? (f) How many permutations of [10] have all of the even numbers appearing in the first seven positions? (9) How many permutations of (10] alternate even and odd numbers?
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