How to convince parent to let friend go on vacation with us?

ok so we might go on a cruise soon...and my brother moved out o he wouldnt go but i wanted my friend to go with us...my father might not go either so it would be me ,my mother, and possibliy my friend. ow do i ask her and convince her. ive never done anything like this before...plus we are 14 years old. my birthday is coming up could i ask if this could be a birthday present for me ?