Assignment3-S2019.pdf - Introduction to Combinatorics Assignment 3 University of Toronto Scarborough Due on March 25 on gradescope by 7pm \u2022 Please

Assignment3-S2019.pdf - Introduction to Combinatorics...

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Introduction to Combinatorics: Assignment 3 University of Toronto Scarborough Due on March 25 on gradescope by 7pm Please answer all problems below and your answers on gradescope. Please indicate on gradescope which portion of your work corresponds to which problem. Problem 1. (15 points) Prove that 1 0 + 2 1 + 3 2 + · · · + n + 1 n = n + 2 n . Problem 2. (5 points) Relate the digits of the powers of 11: 11 , 11 2 , 11 3 , 11 4 with the Pascal triangle. Problem 3. (20 points) Using the theory of linear equations, compute in how many ways can we choose four non-consecutive numbers from the set T 100 = { 1 , 2 , · · · , 100 } . For example, the following four numbers { 1 , 2 , 5 , 7 } cannot be selected because 1,2 are consecutive. Problem 4. (10 points) Imagine that there are 2 n people in front of a box office. Each of n of these people holds a 10 dollar bill and each of the other
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  • Fall '08
  • Combinatorics, English-language films, University of Toronto Scarborough

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