Four cookies are distributed between Tom, Dick, and Harry in such a way that each gets at least one cookie.  The 4 cookies are traditionally represented as "stars" (****).  But here, they are shown as cookie-colored circles (●●●●). The 3 gaps between the cookies are indicated by red caret symbols (^ ^ ^).  With three people, we need 2 bar symbols (| |) to occupy any two of the three gaps.  Hence the problem reduces to finding the binomial coefficient, (32),{\displaystyle {\tbinom {3}{2}},} also known as combination "3-choose-2". Also shown are the three corresponding 3-compositions of 4.
Own work
Guy vandegrift