Also... If there is more than one Fred, and they are all throwing the same party it would be: Freds' party.
Because unicorn start with a 'y' sound. As does university. So you use 'a'. If it's an 'u' sound like up and umbrella, you use 'an'. As you do with all vowel sounds.
It's a fair bit easier than Masculine and feminine words in French or masculine, feminine and neutral words in German where there doesn't seem to be any rhyme or reason as to which word get which gender association.