Question

В тренировочных заплывах участвует одновременно по 4 человека. Сколько различных стартовых четверок может составить тренер, если на тренировке присутствует 9 пловцов? Подробно

Answer 1

Calculation of the Number of Different Starting Quartets in Swim Training

To calculate the number of different starting quartets that a coach can form in swim training with 9 swimmers, we can use the concept of combinations.

In this scenario, the order of the swimmers in the quartet does not matter, and each swimmer can only be in one quartet at a time. Therefore, we need to calculate the number of combinations of 9 swimmers taken 4 at a time.

The formula for calculating combinations is:

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

Where: - n is the total number of items (swimmers) - r is the number of items to be selected (quartet)

Let's substitute the values into the formula:

C(9, 4) = 9! / (4! * (9 - 4)!)

Simplifying the equation:

C(9, 4) = 9! / (4! * 5!)

Now, let's calculate the factorial values:

9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880

4! = 4 * 3 * 2 * 1 = 24

5! = 5 * 4 * 3 * 2 * 1 = 120

Substituting the factorial values back into the equation:

C(9, 4) = 362,880 / (24 * 120)

Simplifying further:

C(9, 4) = 362,880 / 2,880

Finally, performing the division:

C(9, 4) = 126

Therefore, a coach can form 126 different starting quartets in swim training with 9 swimmers.