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?

Name: A permutation of the set [10] = {1, 2, 3, ..., 10} is a wayof listing
Uploaded: 2024-03-05T11:53:49.000Z
Channel: Bartleby
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

See similar textbooks

Related questions

Q: This is a combinatorics math counting problem: Suppose you are trying to create a password for your…

A: As per the question we are given a combinatorics problem, where we are tasked with determining the…

Q: GROUP #1: Fundamental Principle of Counting 1 How many 3-digit numbers can be formed from the digits…

A: Hi! Thank you for the question. As per the honor code, we are allowed to answer 1 question at a…

Q: Find out how many distinguishable permutations are in the following words. Population

A: The given word is "population"

Q: (a) How many three-digit nos. can be formed from the digits 0.1.2.3.4.5 & 6 if each digit can be…

Q: For: 25, 23, 21, 19, 17, .. Find RECURSIVELY An

Q: evaluate each arithmetic seies described (-16)+(-24)+(-32)+(-40)..., n=12

Q: Using the digits 2 through 8, find the number of different 5-digit numbers such that: (a) Digits…

A: Hi thankyou for posting this question, since you have posted multiple subparts as per our policy…

Q: (a) How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6 and 7 such that…

A: Any number which has 0 or 5 in the unit place is divisible by 5. Case 1: when unit digit is 0 The…

Q: (b) How many ways can the letters of the word MAILBOX be arranged in a row if M and A must remain…

A: We use techniques of basic counting to solve this question.

Q: 5. (12 points) Find how many positive integers between 1 and 99, inclusive, have the following…

A: The objective of this question is to find the number of positive integers between 1 and 99 that are…

Q: Let us divide the odd positive integers into two arithmetic progressions; the red numbers are 1, 5,…

Q: This is a combinatorics math counting problem: If σ(1) is not an element of {1, 2} and σ(4) does…

A: As per the question, we are asked to determine the number of permutations of the set [5] that…

Q: 5. (12 points) Find how many positive integers between 1 and 99, inclusive, have the following…

A: The objective of this question is to find the number of positive integers between 1 and 99 that…

Q: (a) How many 2 letter codes can be formed using A, B, C, and D if each letter can be used any number…

Q: (b) How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 and 8 such…

A: Given Digits: 0,1,2,3,4,5,6,7 & 8

Q: (8) How many integers in the set [1,000] = {1, 2, ..., 1,000} are (a) divisible by 5? divisible by…

Q: Consider a set of elements X₁, (a) How many 8-element subsets contain x3? X12. (b) How many…

Q: Is there any derivation of the formula of permutation and combination?

A: Derivation for the formula of permutation and combination . Permutation : (Arrangement of r things…

Q: Select the correct choice that completes the sentence below. The formula for the number of…

A: We want tell you which one is the correct choice.

Q: For these part questions, show your work using factorials. (a) A room consists of 60 people. How…

A: Combination: It means selection from whole . It is denoted by Crn where n is total number objects…

Q: For each natural aumber a, the sum 1(2) + 2(3) ++ R(n + 1) is equal ta None of the choices This…

Q: A "word" is a sequence of 5 letters where each letter comes from the set {a,b,c}. The ordering of…

A: In permutations order is significant. In the first subpart, we have to find how many 5 letter words…

Q: justify each answer. (a) The number 1003 is prime because it is not divisible by 2, 3, 5, 7, 11. (b)…

Q: - Find every positive integer n with the property that 2" - 1 is divisible by n.

Q: (6) Find the sum of the integers for 7 to 508 Tmelusive,

A: first term (a0) = 7last term( an) = 508, d = 1 ( natural no.)first we have to find total no of…

Q: (a) How many different collections of 50 coins can be chosen if there are at least 50 of each kind…

Q: (a) If repetition of digits is not allowed, how many four-digit numbers can be formed using the…

A: Solution: a. The given digits are 1, 2, 3, 4 and 5. Here, the repetition is not allowed.

Q: Number 3

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.

Topic Video

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Given conditions.

VIEW

Solution.

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Permutation and Combination$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

. Let a = 1 2 3 4 5 6 2 1 4 5 6 3 and B = 1 2 3 4 5 6 1 3 2 65 4 :) (a) Find a B(2). Find 6-¹(2). (b) Find a B. State the answer in the array notation. (c) Find 6-¹. State the answer in the array notation. (d) Find a³. State the answer in the array notation. (e) Find 3-2. State the answer in the array notation. be permutations.
Consider numbers of the form a = a₁ª2a3….. an, with n digits, each digit from the set {1, 2, 3, 4, 5, 6, 7, 8}. For example, if n = 4, the number a = a₁ª2ª3a4 will have 4 digits from the set {1,2, 3, 4, 5, 6, 7, 8}. Let n = 7. a. How many such numbers are there? b. How many c. How many such numbers are there for which the sum of the digits is even? such numbers contain more even digits than odd digits?
Given the permutation, [2, 5, 1, 6, 3, 4], and its transpose, [4, 3, 6, 1, 5, 2], find the number of inversions in the permutation and its transpose.
How many ways can one select a subset of 10 elements from {1, 2, 3, . . . , 1000} so that the biggest and smallest elements selected differ by at most 100? Justify your answer.
Discrete Mathematics: Counting. Please check the image for the question.
Consider the set {1,2,3}. i. Write the elements of the permutations by taking two digits from above three ii. Write the elements of the permutation without repetition of the 3 numbers taken all 3 at a time. iii. Do both cases (i) and (ii) have the same number of elements?
Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest value of n for which 2n -1 is not a prime number. Show all your work.
How many numbers are there in the set {1,2,3,...,200} which are divisible by neither 3 nor 4 nor 12?
Prove the handshake theorem. If n people all shake hands with each other, the total number of distinct handshakes is [n(n-1)]/2
(9) How many different two-digit numbers can be made from the digits 3, 5 and 7 if: (a) the digits can be repeated? (b) the digits cannot be repeated? List all possibilities in each case.
(a) Find the order of a modulo 7 for a = 1, 2, 3, 4, 5, 6.