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At a dog show, a German Shepherd, a Golden Retriever, a Dachshund, a Boxer, an Airedale, an Alaskan Malamute, and a Basset Hound won first place in their divisions. In how many different orders could these winners be announced?

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Q. At a dog show, a German Shepherd, a Golden Retriever, a Dachshund, a Boxer, an Airedale, an Alaskan Malamute, and a Basset Hound won first place in their divisions. In how many different orders could these winners be announced?

List of Winners: List of winners: German Shepherd, Golden Retriever, Dachshund, Boxer, Airedale, Alaskan Malamute, and Basset Hound. There are $7$ dogs. $\newline$ Number of orders: $7!$
Calculate Factorial: Calculate $7!$ . $\newline$ $7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$ $\newline$ $= 5040$

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