To find how many ways four people can be arranged in order of height, we need to determine the number of possible permutations of four distinct individuals.

The formula for calculating the number of permutations of $n$ distinct objects is:

$n! = n \times (n-1) \times (n-2) \times \cdots \times 1$

In this case, $n = 4$, so the calculation is:

$4! = 4 \times 3 \times 2 \times 1 = 24$

Therefore, there are 24 ways to arrange four people in order of height from shortest to tallest.

Would you like a detailed explanation of permutations or have any other questions? Here are some related questions to consider:

1. How many ways can five people be arranged in order of height?
2. What is the difference between permutations and combinations?
3. How does the factorial function grow as $n$ increases?
4. What if two people were the same height? How would the number of arrangements change?
5. How can permutations be applied to seating arrangements?

Tip: When solving problems with arrangements or sequences, always check if repetition is allowed, as it impacts the solution method.