(a) In how many ways can the integers 1, 2, 3, . . . , n be...

Question:

(a) In how many ways can the integers 1, 2, 3, . . . , n be arranged in a line so that none of the patterns 12, 23, 34,..., (n - 1)n occurs?
(b) Show that the result in part (a) equals dn-1 + dn. (dn = the number of derangements of 1, 2, 3, ..., n.)

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

See More Books

Question Posted: Jun 21, 2016 08:37 AM

See More Questions

In how many ways can the integers 1, 2, 3,..., 10 be arranged in a line so that no even integer is in its natural position?
Answer part (a) of Exercise 14 if the numbers are arranged in a circle, and, as we count clockwise about the circle, none of the patterns 12, 23, 34, ..., (n - 1)n, n1 occurs. Exercise 14 In how many...
(a) In how many ways can 6 people be lined up to get on a bus? (b) If 3 specific persons, among 6, insist on following each other, how many ways are possible? (c) If 2 specific persons, among 6,...
The HaberBosch process for the production of ammonia is one of the key industrial processes in developed countries. N 2 (g) + 3 H 2 (g) 2 NH 3 (g) (a) Calculate r G for the reaction at 298 K, 800...
Why are good work habits and time management so effective in reducing job stress?
The excess present value index or profitability index is a useful guide when allocating limited funds among projects. Do you agree? Explain.
Explain the analysis of a firm's performance. (p. 435) LO.1
1. What environmental factors could Bill Strickland have changed in his life? 2. What moral authority does Bill Strickland speak from to struggling college students? 3. What impact did Stricklands...
Predetermined Factory Overhead Rate Turbo Shop uses job order costing to determine the cost of performing engine repair work. Estimated costs and expenses for the coming period are as follows: The...
1. Physics is a field of study that governs (a) How the planets orbit the sun. (b) The rate at which blood flows through a persons veins. (c) How quickly a helium balloon will rise into the air. (d)...
Give a combinatorial argument to verify that for all n Z+, (For each 1 k n, dk = the number of derangements of 1, 2, 3, . . . , k; d0 = 1.) In k-
(a) List all the derangements of 1, 2, 3, 4, 5 where the first three numbers are 1, 2, and 3, in some order. (b) List all the derangements of 1, 2, 3, 4, 5, 6 where the first three numbers are 1, 2,...
If you were writing a business plan for Locker Lookz, what would you recommend as an exit strategy? Explain your answer.
Use least square regression to fit a straight line to the following data taken from the conductance (S/m) of a material with respect to temperature (C) of a composite material used to absorb heat....
A pile group consists of nine friction piles in clay soil (see Figure 10-40). The diameter of each pile is 16 in., and the embedded length is 30 ft each. Center-to-center pile spacing is 4 ft. Soil...
The rigid bar EBC is supported by two links AB and CD as shown in Figure 1. The Link AB is made of aluminum (E = 70 GPa) and the link CD is made of steel (E = 200 GPa). Both links have a Width = 30...
a well-insulated storage tank was pressurized under ideal gas conditions by air flowing into the tank. We used the first law to estimate the final temperature of the gas in the tank, Tf,tank- = We...
Transportation of natural gas is commonly done via pipelinesacross long distances. A company uses a 0.6-m diameter pipe totransport natural gas. Then pumping stations are located atdifferent points...
Use the web to look up the density of different forms of steel, such as stainless steel or magnetic steel, and discuss whether or not the differences in the densities follow what might be predicted...
On October 31 Juanita Ortega, owner of Outback Guide Service, received a bank statement dated October 30. Juanita found the following: 1. The checkbook has a balance of $2,551.34. 2. The bank...
Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day)...
Figure 2 . 1 8 shows a network of water pipes with flows measured in liters per minute. (a) Set up and solve a system of linear equations to find the possible flows. (b) If the flow through AB is...
The downtown core of Gotham City consists of one-way streets, and the traffic flow has been measured at each intersection. For the city block shown in Figure 2.19, the numbers represent the average...
Your company BMG Inc. has to liquidate some equipment that is being replaced. The originally cost of the equipment is $120,000. The firm has deprecated 65% of the original cost. The salvage value of...
1. What are the steps that the company has to do in time of merger transaction? And What are the obstacle that may lead to merger failure? 2.What are the Exceptions to not to consolidate the...
Problem 12-22 Net Present Value Analysis [LO12-2] The Sweetwater Candy Company would like to buy a new machine that would automatically "dip" chocolates. The dipping operation currently is done...

(a) In how many ways can the integers 1, 2, 3, . . . , n be...

Question:

Step by Step Answer:

a For 1 i n 1 let c i denote the occurrence of the pattern ii ...View the full answer

Discrete and Combinatorial Mathematics An Applied Introduction

Students also viewed these Linear Algebra questions