QUESTION A
The number of ways that we can pick the medals is given using the permutation:
[tex]^{10}P_3[/tex]The permutation formula is given to be:
[tex]^nP_r=\frac{n !}{(n-r) !}[/tex]Therefore, the number of ways the winner can be chosen is calculated to be:
[tex]^{10}P_3=\frac{10!}{(10-3)!}=\frac{10!}{7!}=\frac{10\times9\times8\times7!}{7!}=720[/tex]Hence, there are 720 ways the medals can be awarded.
QUESTION B
The probability is calculated to be the ratio of the expected outcome to the total possible outcomes:
[tex]P=\frac{Number\text{ }of\text{ }expected\text{ }outcomes}{Number\text{ }of\text{ }possible\text{ }outcomes}[/tex]Picking Susie, Jose, and Thomas in that order is just one possible outcome.
Therefore, the probability of this outcome is:
[tex]P=\frac{1}{720}[/tex]