Question

В высшей лиге по футболу 18 команд. Борьба идёт за золотые, серебряные и бронзовые медали. Сколькими способами медали могут быть распределены между командами?

Answer 1

Размещение без повторений:
А (3,18) =18*17*16 =4896   <---- ответ

Answer 2

Calculation of Medal Distribution

To calculate the number of ways the medals can be distributed among the 18 teams in the top football league, we can use the concept of combinations.

Since there are three types of medals (gold, silver, and bronze), each team can be awarded one of these three medals.

The number of ways the medals can be distributed can be calculated using the formula for combinations. The formula for combinations is:

C(n, r) = n! / (r! * (n-r)!)

Where: - n is the total number of items (teams in this case) - r is the number of items to be chosen (medals in this case) - ! denotes factorial, which means multiplying a number by all the positive integers less than it down to 1

In this case, we have 18 teams and 3 medals to be distributed.

Using the combination formula, we can calculate the number of ways the medals can be distributed among the teams:

C(18, 3) = 18! / (3! * (18-3)!)

Simplifying the equation:

C(18, 3) = 18! / (3! * 15!)

Now let's calculate the value:

C(18, 3) = (18 * 17 * 16 * 15!) / (3 * 2 * 1 * 15!)

The factorials in the numerator and denominator cancel out:

C(18, 3) = (18 * 17 * 16) / (3 * 2 * 1)

Evaluating the expression:

C(18, 3) = 816

Therefore, there are 816 different ways the medals can be distributed among the 18 teams in the top football league.