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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