15-344/Homework Assignment 10: Difference between revisions
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| ⚫ | This assignment is due <span style="color: blue;">at TBA, yet no sooner than Thursday December 10 at 6PM</span>. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong. |
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{{In Preparation}} |
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'''Reread |
'''Reread''' your notes for November 26 through December 3. Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. |
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'''Solve''' |
'''Solve''' and submit your solutions of the following three problems: |
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'''Problem 1.''' What is the probability that a soccer game with <math>2n</math> goals ends with a tie, and that this tie is the first tie in the game (except before the first goal)? |
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'''In addition,''' ... |
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'''Problem 2.''' How many possible histories are there for a soccer game that ends with the score <math>(m,n)</math>, where <math>m>n</math>, if it is known that the first team is never behind the second? |
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'''Problem 3.''' Let <math>n</math> be a natural number. How many sequences of integers <math>0=a_1\leq a_2\leq\ldots\leq a_n</math> are there, such that <math>a_k<k</math> for every <math>1\leq k\leq n</math>? For example, for <math>n=3</math> the allowed sequences are 000, 001, 002, 011, and 012. |
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{{15-344:Dror/Students Divider}} |
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Revision as of 18:10, 3 December 2015
This assignment is due at TBA, yet no sooner than Thursday December 10 at 6PM. Here and everywhere, neatness counts!! You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong.
Reread your notes for November 26 through December 3. Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read.
Solve and submit your solutions of the following three problems:
Problem 1. What is the probability that a soccer game with goals ends with a tie, and that this tie is the first tie in the game (except before the first goal)?
Problem 2. How many possible histories are there for a soccer game that ends with the score , where , if it is known that the first team is never behind the second?
Problem 3. Let be a natural number. How many sequences of integers are there, such that for every ? For example, for the allowed sequences are 000, 001, 002, 011, and 012.
| Dror's notes above / Students' notes below |
