Prove that if n and k are integers with 1 ¤ k ¤ n, then a) Using

Question:

Prove that if n and k are integers with 1 ‰¤ k ‰¤ n, then

a) Using a combinatorial proof.
b) Using an algebraic proof based on the formula for (nr) given in Theorem 2 in Section 6.3.

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

Step by Step Answer:

Related Book For book-img-for-question

Discrete Mathematics and Its Applications

ISBN: 978-0073383095

7th edition

Authors: Kenneth H. Rosen

See More Books

Question Posted: May 03, 2016 01:41 AM

See More Questions

Show that if n and k are integers with 1 ¤ k ¤ n, then
(a) Provide a combinatorial argument to show that if n and k are positive integers with n = 3k, then n!/(3!)k is an integer. (b) Generalize the result of part (a).
Prove that if n ( m, then there is no m ( n matrix A such that ( Ax ( = ((x(( for all x in. IR"
In Exercises 7681, find the domain of each function. g(x) = 4 x - 7
List five ways that management can seek to relax a constraint by expanding the capacity of a bottleneck operation.
What can you learn from the failures you have experienced?
US. airlines fly approximately 48 billion passenger-miles per month and average about 2.63 fatalities per month (Statistical Abstract of the United States: 1998). Assume the probability distribution...
1. What ethical issues is Heather facing in this situation? What possible marketing claims about the companys relationship with the Amazonian tribe would cross a line into unethical territory? What...
What's the major difference between large banks and small banks? Which have had higher returns on assets
Consider FASB standards for mergers and acquisitions by not-for-profit organizations. Answer the following questions: a. What is the difference between a merger and an acquisition? b. What is the...
Prove Pascal's identity, using the formula for C). (n
Prove the identity (nr)(rk) = (nk) (n-kr -k), whenever n, r, and k are nonnegative integers with r n and k r, a) Using a combinatorial argument. b) Using an argument based on the formula for the...
A uniform beam is 5.0 m long and has a mass of 53 kg. In Figure the beam is supported in a horizontal position by a hinge and a cable, with angle = 60?. In unit-vector notation, what is the force on...
Salmone Company reported the following purchases and sales of its only product. Salmone uses a perpetual inventory system. Determine the cost assigned to the ending inventory using FIFO. 1 Date...
A company may go through organizational change at various stages in its life cycle for a variety of reasons. Reasons can include a change in ownership as well as a change in the competitive...
6 (a) Below is a diagram of a rotating disc viscometer (FIGURE 4). Explain its operations and limitations as to use. If, in a similar works situation, it is necessary to make measurements on a...
As part of your role in the Business Analytics and Data Analytics team, you have been asked to forecast Food Retailing as part of a wider report being commissioned by the above collaboration - on...
You are three students who have together bought a business that makes snow. The customers consist of both large public enterprises and private individuals. The business is run all year round, but the...
In Problems 3336, there is a tie for the choice of the first pivot column. Use the simplex method to solve each problem two different ways: first by choosing column 1 as the first pivot column, and...
Do the three planes x + 2x + x 3 = 4, X X 3 = 1, and x + 3x = 0 have at least one common point of intersection? Explain.
Suppose again that Z = X + Y. Find fZ if (a) fx (x) = fy(2) = x/2, if 0
Suppose that X and Y are independent and Z = X + Y . Find fZ if (a) S de-Ar, if r > 0, otherwise. fx (x) = 0, )={ue-H, if z > 0, 0, fr (x) = { otherwise. (b) S de-A, if z> 0, 0, fx(w) = { otherwise....
Suppose that R2 = X2 + Y 2. Find fR2 and fR if fx (x) -e-(e-)/20% V2701 fy (x) V2To2 Eo7/(et-a)-- 2n02
QUESTION 3 A business owns seven flats rented out to staff at R500 per month. All flats were tenanted Ist january 21 months rent was in arrears and as at 31st December 14 months' rent wa Identify the...
1. 2. 3. Select the Tables sheet, select cells A6:B10, and create range names using the Create from Selection button [Formulas tab, Defined Names group]. Select cells B1:F2 and click the Name box....
Tropical Rainwear issues 3,000 shares of its $18 par value preferred stock for cash at $20 per share. Record the issuance of the preferred shares. (If no entry is required for a particular...

Prove that if n and k are integers with 1 ¤ k ¤ n, then a) Using

Question:

k (C) = n).

Step by Step Answer:

a We show that each side counts the number of ways to choose fro...View the full answer

Discrete Mathematics and Its Applications

Students also viewed these Statistics questions