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At a dog show, first-place winners were selected in each of 4 divisions. In how many different orders could these winners be announced?

At a dog show, first-place winners were selected in each of $4$ divisions. In how many different orders could these winners be announced?

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Q. At a dog show, first-place winners were selected in each of

4

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

Count Divisions: List the number of divisions with first-place winners: There are $4$ divisions. $\newline$ We need to find the number of different orders in which these winners can be announced. $\newline$ Since the order matters, this is a permutation problem. $\newline$ Number of orders: $4!$
Permutation Problem: Calculate the value of $4!$ .
Number of orders = $4!$
= $4 \times 3 \times 2 \times 1$
= $24$

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