How to count all files inside a folder, its subfolder and all

[Kaleva]

How to count all files inside a folder, its subfolder and all . The count should not include folder count

I have a really deep directory tree on my Linux box. I would like to count all of the files in that path, including all of the subdirectories.

For instance, given this directory tree:
/home/blue
/home/red
/home/dir/green
/home/dir/yellow
/home/otherDir/