There is a much simpler way than all of these other methods.
find /v /c "" filename.ext
Holdover from the legacy MS-DOS days, apparently. More info here: https://devblogs.microsoft.com/oldnewthing/20110825-00/?p=9803
adb shell pm list packages | find /v /c ""
If your android device is connected to your PC and you have the android SDK on your path, this prints out the number of apps installed on your device.