The probability that the tourist will visit the cities in alphabetical order is 0.00020
Further explanation
The probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation ( Arrangement )
Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination ( Selection )
Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem!
A tourist in Ireland wants to visit seven different cities.
Let's suppose the city is A, B, C, D, E, F, G.
If the route is randomly selected, then the number of ways of visiting all of the cities will be :
[tex]^7P_7 = \frac{7!}{(7 - 7)!}[/tex]
[tex]^7P_7 = \frac{7!}{0!}[/tex]
[tex]^7P_7 = \frac{7!}{1}[/tex]
[tex]^7P_7 = 7![/tex]
[tex]^7P_7 = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1[/tex]
[tex]^7P_7 = 5040[/tex]
To visit these cities in alphabetical order there is only 1 way, namely :
A - B - C - D - E - F - G - H
There are only 1 way from 5040 ways available, so the probability that the tourist will visit the cities in alphabetical order is :
[tex]Probability = \frac{1}{5040}[/tex]
[tex]\boxed {Probability = 0.00020}[/tex] ( in five decimal places )
Learn more
- Rolling a six-sided die : https://brainly.com/question/1637111
- Combined Probability of Two Events : https://brainly.com/question/12745908
- Different Birthdays : https://brainly.com/question/7567074
Answer details
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Permutation , Combination , Alphabetical , Order , Arrangement , Selection
