By Alan Doerr, Kenneth Levasseur
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Textbook from UMass Lowell, model three. 0
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Applied Discrete constructions via Alan Doerr & Kenneth Levasseur is authorized lower than an inventive Commons Attribution-NonCommercial-ShareAlike three. zero usa License.
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Extra info for Applied Discrete Structures
For example, if four numbers, a1 , a2 , a3 , and a4 are to be added, their sum may be written down in several ways, such as ((a1 + a2 ) + a3 ) + a4 or (a1 + a2 ) + (a3 + a4 ). In the first expression, the first two numbers are added, the result is added to the third number, and that result is added to the fourth number. In the second expression the first two numbers and the last two numbers are added and the results of these additions are added. Of course, we know that the final results will be the same.
We can apply the rule of product to get the total number of bridge hands with the following logic. West can get any of the 52 13 hands identified above. Then North get 13 of the remaining 39 cards and so has 39 13 possible hands. 26 East then gets 13 of the 26 remaining cards, which has 13 possibilities. South gets the remaining cards. 4 Sage Note Sage will do the same calculations for bridge hands just as easily. A correct input is provided in the sage cell below. 40 CHAPTER 2. 5 Exercises A Exercises 1.
A person is to complete a true-false questionnaire consisting of ten questions. How many diﬀerent ways are there to answer the questionnaire? Since each question can be answered either of two ways (true or false), and there are a total of ten questions, there are 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 = 210 = 1024 diﬀerent ways of answering the questionnaire. The reader is encouraged to visualize the tree diagram of this example, but not to draw it! We formalize the procedures developed in the previous examples with the following rule and its extension.