For some reason I can not get my head around probability. Please show me how to work the problem not just the answers.

A class has 11 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.)

There are 11! ways to arrange the students.

One of these will be the correct order of shortest to tallest.
So the prob is 1/11! or 1/39916800

(I looked at it, as from shortest to tallest from the left, of course we could also have shortest to tallest from the right. In that case there would be TWO such cases and the prob would be be 2/11!
I will let you decide which interpretation is needed)

I was on that line of thinking as well but there are four possible answers and that doesn't match any of them. The four possible answers are:

A) 0.00000003 ; B) 0.1000 ; C) 0.00000025 ; and D) 0.00000028

I really want to understand how to work these problems but I am so lost.

1/39916800 = .000000025

To solve this probability problem, let's break it down step by step.

Step 1: Determine the total number of possible seating arrangements.
In this case, there are 11 students, and each student can be assigned one of the 11 seats. So, the total number of possible seating arrangements is 11 factorial (11!).

Step 2: Determine the number of favorable outcomes.
Since the students need to be arranged from shortest to tallest, there is only one specific arrangement that satisfies this condition. It means that there is only one favorable outcome.

Step 3: Calculate the probability.
To find the probability, divide the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes

In this case, the probability is:
Probability = 1 / (11!)

Now let's simplify this expression.

11! means 11 factorial. Factorial means multiplying a number by all of the positive integers less than it.

11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Calculating this expression gives us:
11! = 39,916,800

So, the probability of arranging the students in order from shortest to tallest is:
Probability = 1 / 39,916,800

To simplify further, you can express this probability as a decimal or a fraction.