When four people pqrand s were measured for height none of them were the same height and p was roller than s it was also found his height was also higher than q and r which was the average of their hight. Given ge conditions hiw many ways can 4 people be arranged in order of height from shortest to tallest

Given the conditions provided in the problem:

1. Four people: \( P \), \( Q \), \( R \), and \( S \).
2. All four individuals have different heights.
3. \( P \) is taller than \( S \).
4. \( P \)'s height is also greater than the average height of \( Q \) and \( R \).

We need to determine the number of ways the four people can be arranged in order of height from shortest to tallest.

### Analyzing the Problem:

Let’s break down the conditions:

- **Condition 1**: \( P \) is taller than \( S \), which implies \( P \) is not the shortest, and \( S \) is not the tallest.
- **Condition 2**: \( P \) is taller than the average height of \( Q \) and \( R \). This implies that \( P \) is taller than both \( Q \) and \( R \).

Thus, we can conclude that the order must be:
\[ Q, R, S, P \]
where \( P \) is the tallest.

### Conclusion:
The arrangement from shortest to tallest must be \( Q \), \( R \), \( S \), \( P \), so there is only **1 way** to arrange the four people in order of height under the given conditions.

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the solution change if some of the heights were allowed to be the same?
2. How would you calculate the average height if specific heights were given?
3. What if \( P \)'s height was less than the average of \( Q \) and \( R \)?
4. Can you find the total number of ways to arrange four people without any conditions?
5. How would you approach this problem if there were more than four people?

**Tip**: When solving problems involving conditions, break them down step by step to avoid confusion and ensure clarity in the solution.

When four people P, Q, R, and S were measured for height, none of them were the same height. P was taller than S, and it was also found that P's height was higher than both Q and R, whose heights were averaged. Given these conditions, how many ways can the four people be arranged in order of height from shortest to tallest?

Discover how to solve a problem involving the arrangement of four people by height, where specific conditions are given. Learn about inequalities, averages, and combinatorics. A detailed solution explains how to order P, Q, R, and S from shortest to tallest. Suitable for Grades 6-8.

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