Question

Із класу, в якому навчається 18 учнів, вибирають трьох делегатів на шкільну конференцію. Скількома способами це можна зробити?

Answer 1

Ответ:

Пошаговое объяснение:

Здесь сочетания из 18 человек по 3.

C(3,18) = (18*17*16)/(1*2*3) = 3*17*16 = 816 способов.

Answer 2

Number of Ways to Choose Delegates

To determine the number of ways to choose three delegates from a class of 18 students, we can use the concept of combinations. In mathematics, a combination is a selection of items from a larger set without regard to the order of the items.

The formula for calculating the number of combinations is given by:

C(n, k) = n! / (k!(n-k)!)

Where: - n is the total number of items in the set (in this case, the number of students in the class) - k is the number of items to be chosen (in this case, the number of delegates to be selected) - n! denotes the factorial of n, which is the product of all positive integers less than or equal to n

Using this formula, we can calculate the number of ways to choose three delegates from a class of 18 students:

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

Simplifying the expression:

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

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

C(18, 3) = 816

Therefore, there are 816 different ways to choose three delegates from a class of 18 students.