A medical research survey categorizes adults as follows by b

A medical research survey categorizes adults as follows: -by -by -by -for -for gender (male or female) age group (age groups are 18-2 5, 26-35, 36-50, 51+) income (less than 30k/year, 30k-50k/year, 51k-80k per year, more than 80k/year) women only: by whether they have been pregnant (yes/no) 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? Just the number, no explanation.

Solution

gender*age*income sizes=2*4*4=32

then 32*2=64 for previous pregnancy in women and 32*3=96 for status of men undergoing prostate exams

(though it will be tough to find younger men undergoing prostate exams)

In total 64+96=102 categories

then 102*2=204 to have size 2 in each category