Respuesta :
There are 1,320 different ways that the winning paintings could be chosen. so option A is correct.
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?
We can use combinations for this case,
Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items.
As, order is important so we use permutation,
The total no. of students n=12
The selected students r=3
nPr= n!/(n-r)!
= 12!/(12-3)!
= 1,320 different ways
Therefore, option A is correct.
Learn more about combinations and permutations here:
https://brainly.com/question/16107928
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