A certain game show determines its participants by randomly selecting individuals, one after the other, from an applicant pool. If the applicant pool consists of 20 total people evenly distributed from five countries, how many participants need to be selected to guarantee the game show has at least one player from each country?

I tried doing (4C1 +4C2+4C3+4C4)*5 to ensure that at least one person from each country is taken. Please improve my solution and tell me where am I going wrong.

Yes. Hint: itâ€™s closer to a riddle.

There are 5 groups with 4 individuals each. Rephrasing the question, it asks that how many participants are to be picked before we are sure that at least one member from each group has been selected (with 100% probability)

Imagine first 4 made picks belong to country 1, next 4 from country 2, next 4 from country 3 and next 4 from country 4. So 16 picks have been made with no representation from country 5. The chance of getting no representation of country 5 is very small but it does exist. So to be sure, 17 pick has to be made to get that 1 member from country 5 with 100% guarantee that all countries have been represented. hence the answer is 17