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.

Question

What is the sample space showing the possible orders of the other three runners?

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

Answer 1

To determine the sample space showing the possible orders of the three remaining runners (Fran, Gloria, and Imani) after Haley is established as the first runner, we need to find all the possible permutations of these three runners.

The runners are:

• Fran (F)
• Gloria (G)
• Imani (I)

The possible orders for the three runners can be generated by calculating the permutations of F, G, and I.

The permutations are:

1. FGI
2. FIG
3. GFI
4. GIF
5. IFG
6. IGF

Now, since Haley (H) is always the first runner in the relay, we add her to the beginning of each permutation:

1. HFGI
2. HFIG
3. HGFI
4. HGIF
5. HIFG
6. HIGF

Thus, the total sample space, taking Haley as the first runner, is:

S = {HFGI, HFIG, HGFI, HGIF, HIFG, HIGF}

None of the provided options match this result. So, the correct sample space should include all variations with Haley in the first position followed by every permutation of the other three runners.

Therefore, the answer is not found among the options provided.