Answer: The sample space showing the possible orders of the other three runners is
![S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}](https://tex.z-dn.net/?f=S%3D%5C%7BHFGI%2CHGFI%2CHIGF%2CHFIG%2CHGIF%2CHIFG%5C%7D)
Step-by-step explanation:
Since we have given that
Number of runners = 4
Four runners are as follows:
Fran, Gloria, Haley, and Imani.
Since Haley is the first runner in the relay,
So, Sample space showing the possible order of the other three runners.
![S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}](https://tex.z-dn.net/?f=S%3D%5C%7BHFGI%2CHGFI%2CHIGF%2CHFIG%2CHGIF%2CHIFG%5C%7D)
Hence, the sample space showing the possible orders of the other three runners is
![S=\{HFGI,HGFI,HIGF,HFIG,HGIF,HIFG\}](https://tex.z-dn.net/?f=S%3D%5C%7BHFGI%2CHGFI%2CHIGF%2CHFIG%2CHGIF%2CHIFG%5C%7D)