Question

Скільки різних способі можна вибрати з 15 чоловік делегацію в складі 3 чоловік.

Answer 1

$C^3_1_5=\frac{15!}{3!*(15-3)!}=\frac{15*14*13*12!}{3!*12!}=\frac{2730}{6}=455$

Answer 2

Calculation of the Number of Different Delegations

To calculate the number of different delegations that can be formed from a group of 15 people to create a delegation of 3 people, we can use the concept of combinations.

The formula to calculate the number of combinations is:

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

Where: - n is the total number of people in the group (15 in this case) - r is the number of people needed for the delegation (3 in this case) - ! denotes the factorial of a number, which means multiplying all the positive integers from 1 to that number

Let's calculate the number of different delegations:

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

Simplifying the equation:

C(15, 3) = 15! / (3! * 12!)

Using the factorial values:

C(15, 3) = (15 * 14 * 13 * 12!) / (3! * 12!)

The factorial of 3 is:

3! = 3 * 2 * 1 = 6

Simplifying further:

C(15, 3) = (15 * 14 * 13) / 6

Calculating the numerator:

15 * 14 * 13 = 2730

Substituting the values:

C(15, 3) = 2730 / 6

Simplifying the division:

C(15, 3) = 455

Therefore, there are 455 different ways to select a delegation of 3 people from a group of 15 individuals.

Please let me know if there is anything else I can help you with!