Here's why:

* Plain: A plain is a broad expanse of flat land, often with few trees.

* Mountain: A mountain is a large landform that rises high above the surrounding land.

* Desert: A desert is an area with very little rainfall, often characterized by sand dunes or rocky terrain.

While deserts can have flat areas, they are not typically described as plains unless specifically referring to a flat desert region like the "Great Plains" of North America.