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?\no s = {fgi, gfi, ifg}\no s = {fgi, fig, gfi, gif}\no s = {fgi, fig, gfi, gif, ifg, igf}\no 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?\no s = {fgi, gfi, ifg}\no s = {fgi, fig, gfi, gif}\no s = {fgi, fig, gfi, gif, ifg, igf}\no s = {fgi, fig, gfi, gif, hfg, hgi, ifg, igf}

Answer

Answer:

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

Explanation:

Step1: Identify the task

Find permutations of 3 runners.

Step2: Use permutation formula

For 3 distinct objects, number of permutations is $n!=3!=3\times2\times 1 = 6$.

Step3: List permutations

Fran - Gloria - Imani (FGI), Fran - Imani - Gloria (FIG), Gloria - Fran - Imani (GFI), Gloria - Imani - Fran (GIF), Imani - Fran - Gloria (IFG), Imani - Gloria - Fran (IGF).