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The top $4$ students have made it to the final round of judging in the school science fair competition. In how many different orders can the judges rank their posters? $\newline$ $\_\_\_\_$ orders

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Full solution

Q. The top

4

students have made it to the final round of judging in the school science fair competition. In how many different orders can the judges rank their posters?

\newline

\_\_\_\_

orders

Understand the problem: Understand the problem. $\newline$ We need to determine the number of different ways to rank the top $4$ students. This is a permutation problem because the order of ranking matters.
Apply the formula: Apply the formula for permutations. $\newline$ The number of ways to arrange $n$ items is $n!$ ( $n$ factorial), which is the product of all positive integers up to $n$ . $\newline$ Since we have $4$ students, we need to find the value of $4!$ .
Calculate the value: Calculate the value of $4!$ . $\newline$ $4! = 4 \times 3 \times 2 \times 1$ $\newline$ $= 24$
Conclude the solution: Conclude the solution. $\newline$ There are $24$ different orders in which the judges can rank the top $4$ students' posters.

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