Answer:
See explanation
Step-by-step explanation:
You are given the list of 6 presidents. You can arrange them in
[tex]6!=1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6=720[/tex]
different arrangements.
Here we used permuatations (not combinations). The difference between combinations and permutations is ordering. With permutations we care about the order of the elements, whereas with combinations we don’t.
Another way to count the number of arrangements is next:
The first president in the list can be chosen in 6 different ways, the second - in 5 ways (5 presidents left), the third - in 4 ways (4 presidents left), the 4th - in 3 ways (3 presidents left), the 5th - in 2 ways (2 presidents left) and the 6th - in 1 way (only 1 president left). In total,
[tex]6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1=720[/tex]
different arrangements.
Only one of these arrangements is correct, so the probability that an unprepared student will guess the correct order is
[tex]\dfrac{1}{720}[/tex]
There are 720 possible arrangements of the presidents, and an unprepared student has a 0.13% probability of guessing the correct order.
Given that a history pop quiz has one question in which students are asked to arrange the following presidents in chronological order: Hayes, Taft, Polk, Taylor, Grant, and Pierce, to determine the number of possible different arrangements of the presidents and calculate the probability that an unprepared student will guess the correct order, the following combination calculation must be performed:
Therefore, there are 720 possible arrangements of the presidents, and an unprepared student has a 0.13% probability of guessing the correct order.
Learn more about probabilities in https://brainly.com/question/13553988
