The manager can choose a group of 7 posters for a promotion in 1716 ways.
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 a total of
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]
A movie theater has 13 new release movie posters
the manager choose a group of 7 for posters.
When we choose 7 posters, the order does not matter.
So we use a combination
We need to find 7 from 13 new release movie posters.
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.\\\\^13C_7 = \dfrac{13!}{7! \times (13-7)!} ways.\\\\^13C_7 = \dfrac{13!}{7! \times6!} ways.\\\\^13C_7 = 1716[/tex]
The manager can choose a group of 7 posters for a promotion in 1716 ways.
Learn more about combinations and permutations here:
https://brainly.com/question/16107928
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