Question

A tourist in ireland wants to visit seven different cities. if the route is randomly selected, what is the probability that the tourist will visit the cities in alphabetical order? round your answer to five decimal places.

Answer 1

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.

$\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }$

Permutation ( Arrangement )

Permutation is the number of ways to arrange objects.

$\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }$

Combination ( Selection )

Combination is the number of ways to select objects.

$\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }$

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 :

$^7P_7 = \frac{7!}{(7 - 7)!}$

$^7P_7 = \frac{7!}{0!}$

$^7P_7 = \frac{7!}{1}$

$^7P_7 = 7!$

$^7P_7 = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$

$^7P_7 = 5040$

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 :

$Probability = \frac{1}{5040}$

$\boxed {Probability = 0.00020}$ ( in five decimal places )

Learn more

• Rolling a​ six-sided die : brainly.com/question/1637111
• Combined Probability of Two Events : brainly.com/question/12745908
• Different Birthdays : brainly.com/question/7567074

Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Permutation , Combination , Alphabetical , Order , Arrangement , Selection

Answer 2

We have that
n----------> number of cities
the probability that the tourist will visit the cities in alphabetical order is (1/n!)

P=(1/n!)
n!-------------> (7*6*5*4*3*2*1)=5040
therefore
1/5040=0.000198-----------> (five decimal places)--------> 0.00020  (0.020%)

the answer is 0.00020  (0.020%)