Discrete Math -- Sets

Question

I am struggling with thinking about this. Any help would be great!!

A medical research survey categorizes adults as follows:

by gender (male or female)
by age group (age groups are 18-25, 26-35, 36-50, 51+)
by income (less than 30k/year, 30k-60k/year, more than 60k/year)
for women only: by whether they have been pregnant (yes/no)
for men only: by frequency of undergoing prostate exams (frequently, rarely, never).

What minimum size of a set of adults will guarantee that there are two people in it with matching characteristics in all categories? You do not need to explain your answer.

How many different categories are there? Have you heard of the pidgeonhole principle? — Arthur, Oct 02 '14 at 22:18
I have heard of it, but I think the way the problem is laid out might be why I can't seem to understand. — user3320746, Oct 02 '14 at 23:53

mar10 · Answer 1 · 2014-10-03T02:20:22.997

Based on this

PowerPoint Lecture Video for Discrete Math

I believe you would have (choices)

(5)

Woman : Yes

Woman : No

Male : Frequently

Male : Rarely

Male : Never
(4) by age group (age groups are 18-25, 26-35, 36-50, 51+)
(3) by income (less than 30k/year, 30k-60k/year, more than 60k/year)

$$5*4*3=60$$

By the product rule, there are 60 ways of answering this survey. Therefore if,

$$60+1=61$$

61 people were surveyed, two will have matching characteristics.

score -2 · Answer 2 · edited Oct 03 '14 at 20:31

-2

By the Pigeonhole Principle it would be one more than the number of categories, C(5,2)*4*3 = 10*4*3 = 120 => 120 +1 = 121.

edited Oct 03 '14 at 20:31

hardmath

37,015

answered Oct 03 '14 at 18:02

monsterx

1

1

There are actually 543 categories, so the right answer is 60+1. – hardmath Oct 03 '14 at 20:33

Discrete Math -- Sets

2 Answers2