Question

Задача по комбінаториці ДАЮ 50 БАЛІВ Створити бригаду із медичних працівників поліклініки для проведення медогляду у дитсадку можна 450 способами. Відомо, що в неї входять 2 лікаря-педіатра і 2 медсестри. Скільки медичних сестер працює у поліклініці, якщо педіатрів 5?

Answer 1

двух из пяти педиатров можем выбрать из 5!/(3!*2!)=5*4/2=10, с помощью 10 способов, остается 450/10, 45 способов, чтобы выбрать из всех медсестер двух, но т.к. нам неизвестно их количество, обозначим его через их и получим что число способов равное 45, с другой стороны равно х!/(2!(х-2)!)=х*(х-1)/2

х*(х-1)/2=45, умножим обе части на два. получим х²-х-90=0, найдем х

х=(1±√(1+360))/2=(1±19)/2; х= 10; х=-9- такого быть не может, т.к. количество медсестер не может быть отрицательным. Остается только одно решение, т.е. их 10 медсестер.

Answer 2

To solve this combinatorics problem, we need to determine the number of medical nurses working in the clinic given that there are 2 pediatricians and 2 medical nurses in the brigade. We also know that there are 450 ways to create the brigade for conducting medical examinations in the kindergarten.

Let's break down the problem step by step:

Step 1: Determine the number of ways to select the pediatricians

Since there are 2 pediatricians in the brigade, we need to calculate the number of ways to select 2 pediatricians from a total of 5. This can be done using the combination formula:

Number of ways to select 2 pediatricians from 5 = C(5, 2)

Using the combination formula, we can calculate this value:

C(5, 2) = 5! / (2! * (5-2)!) = 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10

So, there are 10 ways to select 2 pediatricians from a total of 5.

Step 2: Determine the number of ways to select the medical nurses

Now that we have determined the number of ways to select the pediatricians, we can calculate the number of ways to select the medical nurses. Since there are 2 medical nurses in the brigade, we need to calculate the number of ways to select 2 medical nurses from the remaining nurses in the clinic.

To calculate this, we subtract the number of ways to select the pediatricians from the total number of ways to create the brigade:

Number of ways to select the medical nurses = Total number of ways to create the brigade - Number of ways to select the pediatricians

Number of ways to select the medical nurses = 450 - 10 = 440

Therefore, there are 440 medical nurses working in the clinic.

Please note that the above solution assumes that all pediatricians and medical nurses are distinct and can be selected individually. If there are any additional constraints or assumptions, please let me know, and I'll be happy to assist you further.