Four runners, fran, gloria, haley, and imani, compete on a relay team. haley is the first runner in the relay. the other runners can run in any order. what is the sample space showing the possible orders of the other three runners?
a) s = {fgi, gfi, ifg}
b) s = {fgi, fig, gfi, gif}
c) s = {fgi, fig, gfi, gif, ifg, igf}
d) s = {fgi, fig, gfi, gif, hfg, hgi, ifg, igf}

 The correct option is

(C) S = {FGI, FIG, GFI, GIF, IFG, IGF}

Step-by-step explanation: Given that four runners, Fran, Gloria, Haley and Imani, compete on a relay team. Haley is the first runner in the relay. The other runners can run in any order.

We are to select the sample space that shows the possible orders of the other three runners.

Since Haley is already the first runner, so we have to choose among Fran, Gloria  and Imani.

If Fran is the second runner, then the possible orders are FGI and FIG.

If Gloria is the second runner, then the possible orders are GFI and GIF.

If Imani is the second runner, then the possible orders are IFG and IGF.

Therefore, the sample space showing the possible orders of the other three runners is

S = {FGI, FIG, GFI, GIF, IFG, IGF}.

Thus, option (C) is CORRECT.

5050

hope this !