patty, quinlan, and rashad want to be club officers. the teacher who directs the club will place their names…

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

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

Answer

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, so order matters.

Step2: List all possible pairs

If we choose the first student as president and the second as vice - president: When Patty is president, vice - president can be Quinlan (PQ) or Rashad (PR). When Quinlan is president, vice - president can be Patty (QP) or Rashad (QR). When Rashad is president, vice - president can be Patty (RP) or Quinlan (RQ).

Answer:

D. $S = {PQ, QP, PR, RP, QR, RQ}$