Question

Сколькими способами 10 футбольных команд могут разыграть между собой золотые,бронзовые и серебрянные медали?

Answer 1

Calculating the Number of Ways to Award Gold, Silver, and Bronze Medals to 10 Football Teams

To calculate the number of ways to award gold, silver, and bronze medals to 10 football teams, we can use the concept of permutations.

In this case, we have 10 teams competing for the medals. The team that finishes first will be awarded the gold medal, the team that finishes second will be awarded the silver medal, and the team that finishes third will be awarded the bronze medal.

To calculate the number of ways to award the medals, we can use the formula for permutations:

nPr = n! / (n - r)!

Where: - n is the total number of items (in this case, the number of teams) - r is the number of items to be selected (in this case, the number of medals to be awarded)

In our case, we have 10 teams and we want to award 3 medals (gold, silver, and bronze). Plugging these values into the formula, we get:

10P3 = 10! / (10 - 3)! = 10! / 7!

Simplifying the equation, we have:

10P3 = (10 * 9 * 8 * 7!) / 7!

The factorial of 7! cancels out, leaving us with:

10P3 = 10 * 9 * 8 = 720

Therefore, there are 720 different ways to award gold, silver, and bronze medals to 10 football teams.