Question

Сколько разных команд можно составить из 11 спортсменов по 8 человек. Команды отличаются хотя бы одним спортсменом.

Answer 1

11*10*9*8*7*6*5*4=6652800
на первое место можно взять одного из 11 человек, на второе одного из 10 и т.к. до восьмого места в команде. 

Answer 2

Calculating the Number of Different Teams

To calculate the number of different teams that can be formed from 11 athletes with 8 members each, where teams differ by at least one athlete, we can use the concept of combinations.

The formula for calculating the number of combinations is:

Number of combinations = n! / (r! * (n-r)!)

Where: - n is the total number of items (in this case, athletes) - r is the number of items to choose (in this case, team members) - ! denotes factorial, which is the product of all positive integers up to that number

Applying the Formula

Using the given values: - n = 11 (total number of athletes) - r = 8 (number of team members)

We can calculate the number of different teams using the formula:

Number of combinations = 11! / (8! * (11-8)!)

Calculating the factorials: - 11! = 39916800 - 8! = 40320 - (11-8)! = 6

Substituting the values: Number of combinations = 39916800 / (40320 * 6) Number of combinations ≈ 165

Therefore, the number of different teams that can be formed from 11 athletes with 8 members each, where teams differ by at least one athlete, is approximately 165.