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To determine the number of ways to award 1st, 2nd, and 3rd place prizes among 25 participants, we can use permutations since the order matters. The number of ways to choose 3 participants from 25 and arrange them in order is given by the formula ( P(n, r) = \frac{n!}{(n-r)!} ). For this scenario, it is ( P(25, 3) = \frac{25!}{(25-3)!} = 25 \times 24 \times 23 = 13,800 ). Thus, there are 13,800 ways to award the prizes.

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