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If there are 18 people in your class and you want to divide the class into programming teams of 3
members, you can compute the number of different teams that can be arranged using this formula
(n!/r!(n−r)!).

Respuesta :

ajeigbeibraheem

Using a combination method to determine how many ways can 18 people be divided into programming teams of 3 members, the number of programming teams can be arranged in 816 ways.

What is Combination?

In mathematical model, a combination is a mathematical approach for calculating the number of potential arrangements in a set of things without taking the order arrangement of the items is into consideration.

It can be expressed by using the formula;

[tex]\mathbf{ _nC_r = \dfrac{n !}{ r!(n-r)! } }[/tex]

where:

  • [tex] \mathbf{ _nC_r = number \: of \: combinations \: \} }[/tex]
  • n = total number of set objects = 18
  • r = number of choosing objects = 3

[tex] \mathbf{ _nC_r = \dfrac{18!}{ 3!(18-3)! } }[/tex]

[tex]\mathbf{ _nC_r = \dfrac{18!}{ 3!(15)! } }[/tex]

[tex] \mathbf{ _nC_r = \dfrac{18 \times \: 17 \times \: 16 \times 15!}{ 3!(15)! } }[/tex]

[tex]\mathbf{ _nC_r = \dfrac{18 \times \: 17 \times \: 16 }{ 3 \times \: 2 \times 1} }[/tex]

= 816 ways

Learn more about combinations here:

https://brainly.com/question/11732255

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