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The top 44 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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Q. The top 44 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
  1. Understand the problem: Understand the problem.\newlineWe need to determine the number of different ways to rank the top 44 students. This is a permutation problem because the order of ranking matters.
  2. Apply the formula: Apply the formula for permutations.\newlineThe number of ways to arrange nn items is n!n! (nn factorial), which is the product of all positive integers up to nn.\newlineSince we have 44 students, we need to find the value of 4!4!.
  3. Calculate the value: Calculate the value of 4!4!. \newline4!=4×3×2×14! = 4 \times 3 \times 2 \times 1\newline=24= 24
  4. Conclude the solution: Conclude the solution.\newlineThere are 2424 different orders in which the judges can rank the top 44 students' posters.

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