Answer:
P (She selects the route of four specific capitals) = [tex]\frac{1}{2686320}=(3.7226)10^{-7}[/tex]
D. No,it is not practical to list all of the different possible routes because the number of possible permutations is very large.
Step-by-step explanation:
Let's start assuming that each route is equally likely to be chosen.
Assuming this, we can calculate P(A) where the event A is ''She selects the route of four specific capitals'' doing the following :
P(A) = Favourable cases in which the route of four specific capitals is selected / Total number of ways in 4 of 42 states
The favourable cases in which the route of four specific capitals is selected is equal to 1 .
For the denominator we need the permutation number of 4 in 42.
The permutation number is defined as :
[tex]nPr=\frac{n!}{(n-r)!}[/tex]
[tex]42P4=\frac{42!}{(42-4)!}=\frac{42!}{38!}=2686320[/tex]
The probability of event A is : [tex]\frac{1}{2686320}=(3.7226)10^{-7}[/tex]
Finally for the other question : The option D is the correct because the number of possible permutations is 2686320 and is very large to be listed.
