For each part below, find a finite automaton M which satisfies the given description. Describe M using both a state diagram and a formal 5-tuple in each part.

(a) The language accepted by M is the set of all binary strings which contain exactly 3 1s.

(b) The language accepted by M is the set of all binary strings which contain at least 3 1s.

(c) The language accepted by M is the set of all binary strings which contain at most 3 1s.