Question

ПОМОГИТЕ, ПОЖАЛУЙСТА Выбрать трех дежурных из учеников класса можно в 9 раз большим числом способов, чем выбрать двух дежурных. Сколько человек в классе? Правильный ответ 29. Помогите с решением!!!

Answer 1

$\displaystyle C_{x}^{3}:C_{x}^{2}=9 \\ \\ \frac{x!}{3!(x-3)!}: \frac{x!}{2(x-2)!}=9 \\ \\ \frac{2(x-2)!}{6(x-3)!}=9 \\ \\ \frac{1}{3}(x-2)=9 \\ \\ x-2=27 \\ \\ x=29$

Ответ: в классе 29 человек.

Answer 2

Problem Analysis

To solve this problem, we need to find the number of students in the class. We are given that the number of ways to choose three monitors is nine times greater than the number of ways to choose two monitors. Let's assume the number of students in the class is 'x'.

Solution

To find the number of ways to choose three monitors, we can use the combination formula: C(x, 3). To find the number of ways to choose two monitors, we can use the combination formula: C(x, 2).

According to the given information, the number of ways to choose three monitors is nine times greater than the number of ways to choose two monitors. So we can write the equation:

C(x, 3) = 9 * C(x, 2)

Let's solve this equation to find the value of 'x'.

Solving the Equation

Using the combination formula, we can write the equation as:

(x!)/(3!(x-3)!) = 9 * (x!)/(2!(x-2)!)

Simplifying the equation:

(x * (x-1) * (x-2)!)/(3! * (x-3)!) = 9 * (x * (x-1)!)/(2! * (x-2)!)

Canceling out common terms:

(x * (x-1))/(3 * 2 * 1) = 9 * (x * (x-1))/(2 * 1)

Simplifying further:

(x * (x-1))/6 = 9 * (x * (x-1))/2

Cross-multiplying:

2 * (x * (x-1)) = 6 * 9 * (x * (x-1))

Simplifying:

2x^2 - 2x = 54x^2 - 54x

Rearranging the equation:

52x^2 - 52x = 0

Factoring out common terms:

52x(x - 1) = 0

Setting each factor equal to zero:

52x = 0 or x - 1 = 0

Solving for x:

x = 0 or x = 1

Since the number of students in the class cannot be zero, the only valid solution is x = 1.

Answer

Therefore, there is only one student in the class.