four runners, fran, gloria, haley, and imani, compete on a relay team. haley is the first runner in the…

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? o s = {fgi, gfi, ifg} o s = {fgi, fig, gfi, gif} o s = {fgi, fig, gfi, gif, ifg, igf} o s = {fgi, fig, gfi, gif, hfg, hgi, ifg, igf}

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? o s = {fgi, gfi, ifg} o s = {fgi, fig, gfi, gif} o s = {fgi, fig, gfi, gif, ifg, igf} o s = {fgi, fig, gfi, gif, hfg, hgi, ifg, igf}

Answer

Explanation:

Step1: List permutations

Since Haley is fixed as first - runner, we find permutations of Fran (F), Gloria (G), and Imani (I). The possible arrangements of three distinct objects are found by considering all possible orderings. The permutations of F, G, and I are: FGI, FIG, GFI, GIF, IFG, IGF.

Answer:

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