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Julian has 6 posters he wants to hang on the wall. How many different ways can the posters be arranged in a row?
Answer:

Julian has $6$ posters he wants to hang on the wall. How many different ways can the posters be arranged in a row? $\newline$ Answer:

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Find the number of outcomes: word problems

Full solution

Q. Julian has

6

posters he wants to hang on the wall. How many different ways can the posters be arranged in a row?

\newline

Answer:

Identify Problem Type: Identify the type of problem. $\newline$ We are asked to find the number of different arrangements of $6$ unique items (posters). This is a permutation problem where order matters and we are arranging all items.
Use Permutation Formula: Use the formula for permutations of $n$ distinct items. $\newline$ The number of ways to arrange $n$ unique items is $n!$ ( $n$ factorial), which is the product of all positive integers up to $n$ . $\newline$ For $6$ posters, the calculation is $6!$ ( $6$ factorial).
Calculate $6!$ : Calculate $6!$ . $6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1$ $6! = 720$
Verify Calculation: Verify the calculation for any mathematical errors. $\newline$ Rechecking the multiplication: $\newline$ $6 \times 5 = 30$ $\newline$ $30 \times 4 = 120$ $\newline$ $120 \times 3 = 360$ $\newline$ $360 \times 2 = 720$ $\newline$ $720 \times 1 = 720$ $\newline$ The calculation is correct.

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