Question

1. a tourist in france wants to visit 8 different cities. if the route is randomly selected, what is the probability that she will visit the cities in alphabetical order? a) 40,320 b) $\frac{1}{8}$ c) $\frac{1}{40,320}$ d) $\frac{1}{64}$ 11) a class has 8 students who are to be assigned seating by lot. what is the probability that the students will be arranged in order from shortest to tallest? (assume that no two students are the same height.) a) 0.1000 b) 0.00019841 c) 0.00024802 d) 0.0000248

Explanation:

Step1: Calculate total number of arrangements

The number of permutations of \(n\) distinct objects is \(n!\). For \(n = 8\), the total number of arrangements of 8 distinct - objects (cities in the first case and students in the second case) is \(n!=8! = 8\times7\times6\times5\times4\times3\times2\times1=40320\).

Step2: Determine the favorable number of arrangements

In both cases (visiting cities in alphabetical order and arranging students from shortest - to tallest), there is only 1 favorable arrangement.

Step3: Calculate the probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So the probability is \(\frac{1}{8!}=\frac{1}{40320}\).

Answer:

1. C. \(\frac{1}{40320}\)
2. C. \(0.000024802\approx\frac{1}{40320}\)