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. (a) How many permutations of (10] are there? (b) How many permutations of (10] are there that put 1,2, 3, 4, 5 in the first five positions in some order? (c) We call a sequence unimodal įif the elements of the sequence increase to some point, and then decrease from there on. So, for example 1,2, 3, 4, 5, 10, 9, 8, 7, 6 is unimodal. How many unimodal permutations of [10] are there?

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. (a) How many permutations of (10] are there? (b) How many permutations of (10] are there that put 1,2, 3, 4, 5 in the first five positions in some order? (c) We call a sequence unimodal įif the elements of the sequence increase to some point, and then decrease from there on. So, for example 1,2, 3, 4, 5, 10, 9, 8, 7, 6 is unimodal. How many unimodal permutations of [10] are there?

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Description: A permutation of the set [10] = {1, 2, 3, ..., 10} is a wayof listing the elements of (10] in order so that each element appears exactly once. The following questionsask about counting the number of permutations of [10] with certain properties. Reme

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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