Question

In how many ways can first, second, and third prizes be awarded in a contest with 415 contestants?

Answer 1

To find the number of ways to award three prizes among 415 contestants, multiply the number of choices for each position: 415 options for first place, 414 for second, and 413 for third, resulting in 71,282,190 permutations.

Step-by-step explanation:

The question posed is about counting the number of ways to award first, second, and third prizes among 415 contestants. This is a problem of permutations since the order matters when giving out prizes. The number of ways to award the first prize is 415, as any of the 415 contestants can win. Once the first prize is awarded, 414 contestants remain for the second prize. For the third prize, 413 contestants remain after the first two prizes have been awarded. Hence, the calculation for the total number of ways to distribute the three prizes is the product of these possibilities: 415 × 414 × 413.

Here is the step-by-step calculation:

1. Select the first prize winner: 415 ways.
2. After awarding the first prize, select the second prize winner: 414 ways.
3. After awarding the second prize, select the third prize winner: 413 ways.

Multiplying these together gives us 415 × 414 × 413 = 71,282,190 possible ways to award the first, second, and third prizes to the contestants.