Answered

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?

A. [tex]\( S = \{FGI, GFI, IFG\} \)[/tex]

B. [tex]\( S = \{FGI, FIG, GFI, GIF\} \)[/tex]

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

D. [tex]\( S = \{FGI, FIG, GFI, GIF, HFG, HGI, IFG, IGF\} \)[/tex]



Answer :

GinnyAnswer
To determine the sample space of the possible orders of the other three runners (Fran, Gloria, and Imani) in the relay team, we need to consider all possible permutations of these three runners.

Given that Haley is always the first runner, we look at the possible ways to arrange Fran (F), Gloria (G), and Imani (I). We can list all the permutations of these three runners.

Here is the list of all possible permutations of F, G, and I:
1. FGI
2. FIG
3. GFI
4. GIF
5. IFG
6. IGF

These permutations represent all the different ways Fran, Gloria, and Imani can be ordered after Haley runs the first leg of the relay.

So, the sample space consists of all these combinations, indicating the different orders they can take. Hence, the correct sample space is:

[tex]\[ S = \{FGI, FIG, GFI, GIF, IFG, IGF\} \][/tex]

Therefore, the correct answer is:
[tex]\[ S=\{F G I, F I G, G F I, G I F, I F G, I G F\} \][/tex]