I am using fedora core 15. How could I download and install flashplayer 15 for fire fox 7.0.1

You can go to Adobe and install the yum version. This will add the Adobe repository, so future updates to flash are automatically available. Then make sure you have the latest flash plugin with (as root):
Alternatively, once the Adobe yum repository has been added, you can use the Add/Remove Software tool to install flash-plugin. Which ever you are most comfortable with.

PS- The current flash plugin version is 11.0.1.152.

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Not to sound rude, but don't you think other people may have asked this question before? Check out the "related threads" box at the bottom of the page, for example. There's a reason the new post page asks you to run a search first, after all.

But in any case it's easy. You don't even need a special package (although they do provide the extra convenience of handling it with your package manager). Just download the current .tar.gz package from adobe, unpack it, and copy the libflashplayer.so file to one of the directories FF looks in for plugins (google for it). The only other thing you need to do is ensure there aren't any other conflicting versions sitting in one of the other locations.

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Wonders why no one bothers to Google or look at the docs for whatever distro they are running. I am guessing it has to do with a windows mindset.

Very first link when searching for "fedora firefox flash"
Flash - FedoraProject - https://fedoraproject.org/wiki/Flash

I used yum to install flashplayer. Fire fox is still telling me I need the flashplayer plugin. How can I link firefox to the flashplayer plugin?

no kidding ,i lost count of the times o pointed to the fedora documentation
-- the very lengthy and long documentation --
http://docs.fedoraproject.org/en-US/index.html
the bold yellow link in the middle top of the fedoraforum
"Fedora Set-Up Guides"
http://www.fedoraforum.org/
or
Mjm's
http://www.mjmwired.net/resources/mj...f15.html#flash

HOW did you install ff7 ?
by hand or the recommended way
ff7 is in the fedora repos

if by hand then reinstall it using yum
the manual install DOSE NOT have a "plugins" folder , so NO plugins

delete the manually installed version
then

as to flash
fedora uses what is called " alternatives " so that more than one and /or different versions can be installed at the same time