Question

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? o s = {pqr} o s = {pqr, pro, qpr, qrp, rpq, rqp} o s = {pq, pr, qr} o s = {pq, qp, pr, rp, qr, rq}

Explanation:

Step1: Understand sample - space concept

The sample space is the set of all possible outcomes. Here, we are choosing 2 students out of 3 (Patty - P, Quinlan - Q, Rashad - R) for president and vice - president positions. The order of selection matters as the first - chosen is president and the second is vice - president.

Step2: List all possible pairs

If Patty is chosen first, the pairs are (P, Q) and (P, R). If Quinlan is chosen first, the pairs are (Q, P) and (Q, R). If Rashad is chosen first, the pairs are (R, P) and (R, Q). In set notation, these pairs are written as PQ, QP, PR, RP, QR, RQ.

Answer:

S = {PQ, QP, PR, RP, QR, RQ}