(a) The sample space is all possible outcomes of the event. Written in set notation, the sample space for the three runners, A,B, and C finishing the race is: {ABC, ACB, BAC, BCA, CAB, CBA}. There six distinct possible ways for the runners to cross the finish line.

(b) The sample space is all possible ways of the first two runners crossing the finish line. This is: {AB, AC, AD, BA, BC, BD, CA, CB, CD, DA, DB, DC}. There are 12 distinct possible ways for any two of four runners to cross the finish line first.