solve this problem by the Pigeonhole Principle The number of

solve this problem by the Pigeonhole Principle.

The number of countries is 194. Assume the airplane carries six hundred passengers. Prove that among 600 passengers, at least one country is represented by at least four passengers.

Solution

Pigeon Hole Principle

If there are n holes and (n+1) pigeons, then there exists atleast one hole which will have two pigeons

Assuming countries as holes = 194

Assuming passengers as pigeons = 600

Since 194 *3 = 591, hence if we start filling evenly in all the holes, then there will be 3 passengers of each country with 9 passengers still left out of 600

Hence the remaining 9 passengers will go in either of 194 holes, hence by pigeon hole principle there exists at least one country that is represented by at least four passengers