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, cap s , for this event?
Answer
A
cap s is equal to PQR comma PRQ comma QPR comma QRP comma RPQ comma RQP
B
cap s is equal to PQ comma PR comma QR
C
cap s is equal to PQ comma QP comma PR comma RP comma QR comma RQ
D
cap s is equal to PQR
Explanation
Each outcome must record both the president and the vice president, so the order matters. With three students, the possible ordered pairs are PQ, QP, PR, RP, QR, and RQ. Choice D lists all six outcomes; choice C leaves out which student is chosen first.
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