Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president. Which choice represents the sample space, S, for this event? S = {PQR} S = {PQR, PRQ, QPR, QRP, RPQ, RQP} S = {PQ, PR, QR} S = {PQ, QP, PR, RP, QR, RQ}

P = Pat Q = Quinlan R = Rashad

now, the teacher is going to draw out of the hat one first, without replacement, and then draw another one. The first one will be the president, and that could be P, Q or R, and the second one is the Vicepresident, and since one has already being drawn, that could only be two fellows.

so it can be either PQ or QP, president and vice respectively, or PR or RP, same order, or QR or RQ, same president and vice respectively.

thus the total of likely outcomes is PQ, QP, PR, RP, QR, RQ, one paired up with either of the two remaining in the hat.