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?

S = {PQR}
S = {PQR, PRQ, QPR, QRP, RPQ, RQP}
S = {PQ, PR, QR}
S = {PQ, QP, PR, RP, QR, RQ}

Answer 1

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

Explanation:

got it right on edge 2023

Answer 2

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

Explanation:

We have 3 friends:

Patty (who we can represent with the letter P)

Quinlan (who we can represent with the letter Q)

Rashad (who we can represent with the letter R)

There are two positions, that can be represented as:

First-Second.

Where "first" refers to the student whose name is chosen first, this student will be the president.

"second" refers to the student whose name is chosen second, this student will be the vice president.

For example:

PQ

refers for the case where Patty is the president and Quinlan is the vice-president.

Notice that PQ is different than QP.

The sample space will be the set of all the possible combinations of the elements (P, Q, and R) of the form First-Second, which are just the permutations:

PQ, QP, PR, RP, QR, RQ

Then the sample space is:

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

The correct option is the last one.