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At a dog show, first-place winners were selected in each of $5$ 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

5

divisions. In how many different orders could these winners be announced?

\newline

\_\_\_\_\_

orders

Understand the problem: Understand the problem. $\newline$ We need to determine the number of different orders in which the first-place winners of $5$ divisions can be announced. This is a permutation problem where order matters and we are arranging $5$ unique items (winners).
Apply the formula: Apply the formula for permutations. $\newline$ The number of different orders in which we can arrange $n$ items is given by $n$ factorial, denoted as $n!$ . $\newline$ Since we have $5$ winners, the number of different orders is $5!$ .
Calculate the value: Calculate the value of $5!$ . $\newline$ $5! = 5 \times 4 \times 3 \times 2 \times 1$ $\newline$ $= 120$

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