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Karla is creating a survey with 6 questions. She suspects that the order of the questions may influence the responses, so she wants to create multiple versions of the survey with the same 6 questions in different orders.
How many unique ways are there to arrange the questions?

Karla is creating a survey with $6$ questions. She suspects that the order of the questions may influence the responses, so she wants to create multiple versions of the survey with the same $6$ questions in different orders. $\newline$ How many unique ways are there to arrange the questions?

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Counting principle

Full solution

Q. Karla is creating a survey with

6

questions. She suspects that the order of the questions may influence the responses, so she wants to create multiple versions of the survey with the same

6

questions in different orders.

\newline

How many unique ways are there to arrange the questions?

Problem Understanding: Understand the problem. $\newline$ We need to find the number of unique ways to arrange $6$ questions. This is a permutation problem because the order of the questions matters.
Permutation Formula: Apply the formula for permutations. $\newline$ The number of ways to arrange $n$ items is $n$ factorial, denoted as $n!$ . $\newline$ For $6$ questions, the number of unique arrangements is $6!$ ( $6$ factorial).
Calculating $6$ Factorial: Calculate $6$ factorial. $\newline$ $6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1$ $\newline$ $6! = 720$
Verification of Calculation: Verify the calculation. $\newline$ Double-check the multiplication to ensure there are no errors. $\newline$ $6 \times 5 = 30$ $\newline$ $30 \times 4 = 120$ $\newline$ $120 \times 3 = 360$ $\newline$ $360 \times 2 = 720$ $\newline$ $720 \times 1 = 720$ $\newline$ The calculation is correct.

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