I realize that there are 7 iphones, so when I place them with a spot between each one of them, then there are 8 spots in total. Can I do $$\binom{8}{5}7!? $$
how many ways are there to place 7 iPhones and 5 galaxies in a row such that no galaxies are next to each other?
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$\begingroup$
combinatorics
discrete-mathematics
2 Answers
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$7!$ ways to arrange the iPhones.
$\binom85$ ways to choose spots for the Galaxies.
$5!$ ways to arrange the Galaxies.
So in total, there are $7!\times\binom85\times5!$ ways.
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$$\binom{8}{5}.7!.5! $$ the phones themselves can switch places