$($Formal Proof$)$

Based on the sketch given, create a well written solutions to: There are two conventions going on at the RBC Centre at the same time, there is the Clown Convention and the Mime meeting. So$,$ every person in line at the coffee shop is either a clown or a mime. Show $($using mathematical induction$),$ that every time the line has $2$ or more people in it$,$ if the first person is a mime and the last person is a clown then there is some place in the line where a mime is directly in front of a clown.