Countifs - Criteria= contains value in "X:X"

I am trying to count all the cells that contain the contents of another cell. For example:

Column B:
Deep
Limo Service
Classic

Column C:
Classic 333
Limo Service 1A1
Classic 121
Deep. Inc 111

I want to count how many cells in column C contain a value listed in column B.

Current formula, which obviously doesn't work: =COUNTIF(C:C,B:B)

Hope this makes sense... Any help is greatly appreciated!!

Try

=SUMPRODUCT(COUNTIF(C2:C5,"*"&B2:B4&"*"))