Discrete mathematics Document1 - Microsoft Word (Product Activation Failed)FileHomeInsertPage LayoutReferencesMailingsReviewViewa ?A Find -6.% Cut-章 TCalibri (Body) - 11A AAaAalAaBbCcDc AaBbCcDc AaBbC AaBbCc AaB AaBbCcLE CopyСopya ReplacePasteB I U -abe x, x AabAI NormalI No Spaci. Heading 1Heading 2ChangeTitleSubtitleFormat PainterStyles - Select -ClipboardFontParagraphStylesEditingL• 2:1: 1:| 3:1' 4: ·5.1 6.1:7 l:8: 1'9 ' 10: 1 '11: 1'12 :L·13:1' 14:' 15. LA:L 17:L · 18.QUESTION 4Use the extended pigeonhole principle to show that there is at least 15 ways to choose 4 integers from 1to 12 so that all the choices have the same sum.Wall07:53 AM2021-09-20 Page: 1 of 1B I E E E 90% eWords: 0+

Answered: Use the ertended pigeonhole principle…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Pigeonhole principle

If if k+1 pigeons are assigned to k pigeonholes, then there is at least one pigeonhole containing two or more pigeons.

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Number of ChildrenTable 1 shows the number of women (per 1000) between 15 and 50 years of age who have been married grouped by the number of children they have had. Table 2 gives the same information for women who have never been married.1 Number of Children Women per 1000 0 162 1 213 2 344 3 182 4 69 5+ 32 Table 1 Women who have been married Number of Children Women per 1000 0 752 1 117 2 72 3 35 4 15 5+ 10 Table 2 Women who have never been married 1http://www.census.gov/hhes/fertility/data/cps/2014.html, Table 1, June 2014. Condition gt requires numbers instead of "null" and "0" (a) Without doing any calculations, which of the two samples appears to have the highest mean number of children? Women who have been marriedWomen who have never been married Which of the distributions appears to have the mean most different from the median? Women who have been marriedWomen who have never been married…
Student ID Math Score Project Score Age (years) Sex 001254 52 75 15 M 003256 78 89 15 F 001547 92 82 18 F 012589 91 66 17 M 021475 72 93 14 M 032658 46 76 13 M 009561 68 76 14 F 008654 52 82 12 F 008561 83 75 16 M 003547 45 78 14 F 047452 73 96 14 M 041212 64 79 13 F 032320 41 67 13 F 000258 77 72 15 F 001478 82 75 17 M 019521 59 83 15 M 017451 80 71 17 F 016335 48 76 13 M 002474 57 80 14 F 095844 97 71 18 F 097304 86 86 17 M 090024 75 85 15 F 034702 81 80 16 F 001910 67 74 14 F 006454 86 77 17 M 087478 63 82 13 M 078474 68 79 14 F 000977 54 89 12 M 063010 91 73 18 M 007406 46 77 15 F 025740 93 85 17 M…
Quality Control: A company has four photocopy machines A, B, C and D. The probability that a given machine will break down on a particular day is P(A) = %50 P(B) = 15 P(C) = 1⁹/100 P(D) = 11/100 Assuming independence, what is the probability on a particular day that all machines will break down? O 0.00000360 O 0.01000000 O 0.13290803 O 0.00075240 O 0.00132908
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Male Female 27,767 20,516 17,413 24,972 6,080 4,900 28,523 17,661 25,137 11,901 9,821 17,562 21,857 9,865 16,491 21,047 27,687 12,095 23,361 20,089 12,272 16,244 9,584 14,395 13,562 15,467 23,151 23,501 20,071 5,715 142 19,698 21,957 21,640 8,722 18,345 21,058 16,616 17,940 15,249 15,001 28,849 20,938 6,825 6,151 17,111 8,370 4,197 27,687 12,989 11,589 16,879 12,021 13,322 13,709 20,292 12,888 19,417 17,879 14,061 13,743 32,349 11,268 8,738 22,102 10,475 16,788 11,971 10,387 28,702 13,809 22,947 15,644 16,386 11,044 20,101 17,933 20,564 11,413 14,483 11,842 17,349 6,794…
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Use the ertended pigeonhole principle to show that there is at least 15 ways to choose 4 integers from 1 to 12 so that all the choices have the same sum.

Pigeonhole principle