Unit 16 Problem 5 : Discrete Mathematics O Chris Brown,Tyga-Bette My ASU × y WeB

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Unit 16 Problem 5 : Discrete Mathematics

O Chris Brown,Tyga-Bette My ASU × y WeBWorK : Boerner MA × C Secure https://webwork asu.edu/webwork2/Boerner MAT 243 ONLINE A Fall 2017/Unit16 Pigeonhole Principle/5/?key=HNuolTpRyLUk45z4 NOL2wEG1k612Wq&effectivelser; = at all n webwork/ boerner_mat_243_online_a fall_2017/unit16_pigeonhole_principle/5 MAIN MENU Courses Homework Sets Unit16 Pigeonhole Principle Unit16 Pigeonhole Principle: Problem 5 Problem 5 PreviouS Problem List Next User Settings Grades (1 point) A computer is printing out subsets of a 6 element set (possibly including the empty set) Problems (a) At least how many sets must be printed to be sure of having at least 3 identical subsets on the list Answer = Problem 1 Problem 2 Problem 3. Problem 4 Problem 5 (b) At least how many identical subsets are printed if there are 257 subsets on the list? Answer : Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 1 time. Your overall recorded score is 0% You have unlimited attempts remaining Page generaled at 09/27/2017 at 11 22am MST WeBWork1996-2016 | theme: math4 | ww_version: 2.12 pg_version: 2 121 The WeBWorK Project 11:26 AM O Type here to search 91272017

Explanation / Answer

Total no. of possible subsets of 6 elements (including empty set)
= 6C0 + 6C1 + 6C2 + 6C3 +6C4 + 6C5 + 6C6 = 1 + 6 +15 + 15 + 6 + 1 = 44

a). no. of subset to ensure at least 3 identical subsets = 32 * 2 + 1

= 65


b). 257 = 32 * 8 + 1

so, at least 9 identical subsets are printed.

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