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: Use permutation formula

The number of permutations of \(n\) distinct objects is \(n!\). Here \(n = 3\) (Fran, Gloria, Imani), and the formula for permutations of \(n\) objects is \(P(n,n)=\frac{n!}{(n - n)!}=n!\). So \(3! = 3\times2\times1=6\).

Step2: List out permutations

The three - runner combinations are: Fran - Gloria - Imani (FGI), Fran - Imani - Gloria (FIG), Gloria - Fran - Imani (GFI), Gloria - Imani - Fran (GIF), Imani - Fran - Gloria (IFG), Imani - Gloria - Fran (IGF).

Answer:

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