Final answer:
To award first, second, and third prizes in a contest with 185 contestants, there are 6,259,220 ways to do so by multiplying the sequential choices for each prize.
Step-by-step explanation:
Calculating the number of ways first, second, and third prizes can be awarded in a contest with 185 contestants involves a concept in mathematics known as permutations, where order matters. When awarding three distinct prizes, we must consider each prize as a unique position that can be filled by any of the contestants.
To determine the number of ways to award the first prize, there are 185 possible choices. Once the first prize has been awarded, there are 184 contestants remaining for the second prize, and after that, 183 contestants are left for the third prize. These choices constitute sequential events, where each choice reduces the pool of available contestants for the next prize.
We use the fundamental counting principle and multiply the number of choices for each prize: 185 choices for the first prize × 184 choices for the second prize × 183 choices for the third prize equals 6,259,220 total ways to award the first three prizes.