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Answered

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There are 12 paintings at an art show. Three of them are chosen randomly to
display in the gallery window. The order in which they are chosen does not
matter. How many ways are there to choose the paintings?

Sagot :

Answer:

220

Step-by-step explanation: a p e x

There are 220 ways to choose the paintings.

What is combination in mathematics?

"Combination  determines the number of possible arrangements in a collection of items where the order of the selection does not matter."

Formula for combination:

[tex]^{n}C_r=\frac{n!}{r!(n-r)!}[/tex]

For given example,

There are 12 paintings at an art show.

⇒ n = 12

Three of them are chosen randomly to display in the gallery window.

⇒ r = 3

So, using the formula for combination, the number of possible ways to choose the paintings would be,

[tex]\Rightarrow~ ^{n}C_r=\frac{n!}{r!(n-r)!}\\\\\Rightarrow~ ^{12}C_3=\frac{12!}{3!(12-3)!}\\\\\Rightarrow~ ^{12}C_3=\frac{12!}{3!\times 9!}\\\\\Rightarrow~^{12}C_3=220[/tex]

Therefore, there are 220 ways to choose the paintings.

Learn more about combination here:

https://brainly.com/question/13387529

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