Respuesta :
If there are 8 pieces to choose from, there are 1,680 different ways distinct displays are possible.
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?
[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 (all distinct).
To find the Ways can 8 pieces of art in the front window be arranged in the display window.
Let us use permutation to find the number of ways can 8 pieces of art in the front window be arranged in the display window.
here we have
n= 8
r= 4
substituting the values,
[tex]^nC_r = \dfrac{n!}{ (n-r)!}\\\\^8C_4 = \dfrac{8!}{ (8-4)!}\\\\^8C_4 = \dfrac{8!}{ (4)!}\\\\^8C_4 = 8 \times 7 \times 6\times 5\\\\^8C_4 =1680[/tex]
Learn more about combinations and permutations here:
https://brainly.com/question/16107928
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