The members of a group travelling to Venice were offered by their travel agency 4 additional disjoint options of their choice.
Knowing that each option was selected by 80% of the members, what minimal percentage p choose ALL THE 4 OPTIONS?
If 80% of the members chose an option then the remaining 20% did not choose that option.
The minimum percentage of people who took all four options is the complement to the maximum percentage of people who did not take all four options.
Four options each with 20% not taking the option means that at most 20%*4=80% did not take some option. This maximum occurs when the members not taking each option are four disjoint groups (nobody chose to not take two or more options).
Then that leaves a minumum of 100%-80%=20% of members who took all four options.
Solution
