sitting arrangement in single row
Understand the Problem
The question is asking about the concept of sitting arrangements where individuals are arranged in a single row. This topic usually falls under combinatorial mathematics, which looks at how we can arrange items in specific formats.
Answer
The number of arrangements for $n$ individuals is $n!$.
Answer for screen readers
The number of arrangements for $n$ individuals is $n!$.
Steps to Solve
- Identify the total number of individuals
Determine the total number of individuals to arrange. Let's denote this number as $n$.
- Determine the formula for arrangements
In combinatorial mathematics, the total number of ways to arrange $n$ individuals in a single row is given by the factorial of $n$, denoted as $n!$.
- Calculate the factorial
If you are given the total number of individuals, you will need to compute the factorial. For example, if there are 5 individuals, you compute:
$$ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 $$
- Present the result
Once the factorial is calculated, that result represents the number of possible arrangements in a single row.
The number of arrangements for $n$ individuals is $n!$.
More Information
The factorial function is the product of an integer and all the integers below it. It's a fundamental concept in permutations and combinations, commonly used in probability and statistics.
Tips
- Forgetting to consider that $0! = 1$. This means that there is one way to arrange zero individuals (by doing nothing).
- Incorrectly calculating the factorial, especially for larger numbers. Make sure to multiply downwards from the number to 1.
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