Question

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}

Explanation:

Step1: Identificar los elementos a ordenar

Tenemos a Fran (F), Gloria (G) e Imani (I) que se deben ordenar.

Step2: Enumerar permutaciones

Para tres elementos, las permutaciones son:

• Comenzando con F: FGI, FIG
• Comenzando con G: GFI, GIF
• Comenzando con I: IFG, IGF

Así, el espacio muestral S es {FGI, FIG, GFI, GIF, IFG, IGF}.

Answer:

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