Try this method.....

There are 2 versions of Flash, one for IE only (ActiveX version) and on for most other browsers including Firefox (Plugin version). You must update each one individually.

1. using Firefox download and save Flash from this link (save to your Desktop; easier for you to find): get.adobe.com/flashplayer
2. when the download is finished, close Firefox (click Firefox button > Exit OR File > Exit, if using the Menu Bar)
3. click or double-click the file you just downloaded
4. on the left side of the install window, put a check mark in the box next to "I have read and agree"
5. click on the Install button on the lower right of the install window; it will light up after you put the check mark in the previous step
6. let the installation complete; it is quick
7. using Firefox test your installation of Flash here: http://www.adobe.com/software/flash/about/
8. to update IE Flash, follow the same steps but use IE to go to the link in step #1

See Updating Flash in Firefox

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Not related to your question, but....

You need to update some plug-ins:

• Plug-in check: https://www-trunk.stage.mozilla.com/en-US/plugincheck/
• Adobe PDF Plug-In For Firefox and Netscape: Installing/Updating Adobe Reader in Firefox

Thanks very much for responding. In the meantime I went to Adobe's troubleshooting page, and followed the instruction to uninstall the previous version. I did that and noticed that the failed version 10 install was listed, and tried to uninstall that--same problem: close Firefox. So I rebooted Windows, then went to the uninstall page and uninstalled ver 10. That worked fine. Then I installed ver 10 with no problem. Somehow Firefox was staying open as far as Adobe install/uninstall programs were concerned. And the failed version of 10 was also preventing the install. I also installed the latest Reader. Thanks again. I hope all this helps Firefox somehow.