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ffprobe - Streams - Get the number of available streams

ffprobe input -show_entries format=nb_streams -v 0 -of compact=p=0:nk=1
 
or 
 
ffprobe <input> -show_entries format=nb_streams -v 0 -of compact=p=0:nk=1

NOTE: This can be filtered for only video or audio streams by adding -select_streams v or -select_streams a, respectively.