How many paths

there are 8 gates and pass them are 6 ticket booths.  Pass them are 4 different paths to the music show.  How many different wsys to the show.
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Assume that the show is accessible through any gate, ticket booth and path, and that you can access any ticket booth through any gate, and any path through any ticket booth, then the number of ways to the show is 8*6*4=192.

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