Question

I have 3 red, 2 green, and 5 silver plates. In how many ways can I stack these so that no red plate appears on top of a silver plate?

Answer 1

This problem is solved using the Inclusion-Exclusion principle :

Answer = Total ways - Stacks in which exactly one red plate appears on top of a silver plate + Stacks in which exactly two red plates appears on top of two silver plates - Stacks in which all the three red plates appears on top of three silver plates

$=(10!/(5!3!2!)) -(9!/(2!2!4!)) + (8!/(2!2!3!))-(7!/(2!3!2!))$

$=7*5*6=210$