Answer
a. 720
b. 24
c. 1/30
Step-by-step explanation
a. To find in how many ways can they arrive we need to calculate the number of permutations.
The number of permutations of n things chosen r at a time is found using:
[tex]nPr=\frac{n!}{(n-r)!}[/tex]In this case, we have n = 6 people, and we have to choose r = 6 of them. The number permutations is:
[tex]_6P_6=\frac{6!}{(6-6)!}=\frac{6!}{0!}=\frac{6!}{1}=720[/tex]b. If Maria arrives first and Sarah last, then there are 4 places to select randomly (from 2nd to 5th) and 4 people to be ordered. Therefore, we have n = 4 people, and we have to choose r = 4 of them. The number permutations is:
[tex]_4P_4=\frac{4!}{(4-4)!}=4!=24[/tex]c. The probability that Maria will arrive first and Sarah last is calculated as follows:
[tex]\begin{gathered} p=\frac{number\text{ of ways Maria arrives first and Sarah last}}{\text{ Total }number\text{ of ways people can arrive}} \\ p=\frac{24}{720} \\ p=\frac{1}{30} \end{gathered}[/tex]