Answered: (a) J₁ J5 4 2 1 6 3 2 3 A3 7 6 5 8 A4 |…

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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Solve the following problems: (a) How many ways can a store manager arrange a group of 1 team leader and 3 team workers from his 25 employees? (b) A state's license plate has 7 characters. Each character can be a capital letter (A – Z), or a non-zero digit (1 – 9). How many license plates start with 3 capital letters and end with 4 digits with no letter or digit repeated? (c) How many binary strings of length 5 have at least 2 adjacent bits that are the same ("00" or "11") somewhere in the string?
This question is about Perfect Codes in Coding Theory: You may use that a perfect code of length 13 and distance 3 exists over GF(3). A soccer betting form contains a list of 13 matches. Next to each listed match there are three fill-in boxes which correspond to the following three possible guesses: “first team wins”, “second team wins” or “tied match”. The bettor checks one box for each match. Describe a strategy for filling out the smallest number of forms so that at least one of the forms contains at least 12 correct guesses. How many forms need to be filled out under this strategy?
Use simplex algorithm to solve the following question. Max 80x1+20x2+20x3 s.t. 10x1+4x2+x3≤50 6x1+2x2+3x3≤24 10x1+4x2+2x3≤18 x1,x2,x3≥0
Answer the following question accordingly:
As the customer base at OHaganBooks.com grows, IT manager Ruth Nabarro is thinking of introducing identity codes for all the customers, using capital letters and/or numbers. Help her answer the following question. It appears that Nabarro has finally settled on codes consisting of two letters followed by two digits. For technical reasons, the letters must be different, and the first digit cannot be a zero. How many different customers can be identified?
Please include justifications for each step.

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