When connecting your Facebook page to the Sweepstakes Campaign, you do need to connect your personal page that is listed as an Admin on the page. When you are trying to connect them, are you using your Facebook login credentials for your personal page? Once you get through the section to accept the permissions you should be able to choose the page you wish to post the sweepstakes to. This page will display all of the pages you have the required permissions to add the sweepstakes to, if the page you are looking for is missing you might need to update the access level your account has with that page.
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