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At a dog show, first-place winners were selected in each of 55 divisions. In how many different orders could these winners be announced?\newline_____\_\_\_\_\_ orders

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Q. At a dog show, first-place winners were selected in each of 55 divisions. In how many different orders could these winners be announced?\newline_____\_\_\_\_\_ orders
  1. Understand the problem: Understand the problem.\newlineWe need to determine the number of different orders in which the first-place winners of 55 divisions can be announced. This is a permutation problem where order matters and we are arranging 55 unique items (winners).
  2. Apply the formula: Apply the formula for permutations.\newlineThe number of different orders in which we can arrange nn items is given by nn factorial, denoted as n!n!.\newlineSince we have 55 winners, the number of different orders is 5!5!.
  3. Calculate the value: Calculate the value of 5!5!. \newline5!=5×4×3×2×15! = 5 \times 4 \times 3 \times 2 \times 1\newline=120= 120

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