6th Birthday - Giving Out Invitations And How Many 'Nos' To Expect

So this is the first time DD1 has had a birthday party requiring invitations and I'm a bit clueless.

All the invitees are classmates. She's generally pretty responsible so is it OK for me to entrust the invitations to her to hand out or should I give them to her teacher? I'd prefer not to do the latter as that will entail taking DD2 into the classroom with me which results in a meltdown because she won't want to leave. Or I could ask DD1 to give them to her teacher.

Secondly, the swimming pool has a minimum of 10 children for a party. I figured there'd be a few people who can't come so I've invited 14. Does that sound about right?

We gave them to the teacher, but dd has a satchel so we put them in there. I did this as dd missed out on one of the class birthdays as the boy handing them out somehow missed giving her one. We invited 12 girls all intended on coming but one was sick on the day. It was a fairy party so they were all keen to come but I didn't expect them all to come.

Sadly I have found that many parents don't even bother responding to an invite and some show up and some just don't. I make it a rule now that I hand them out with The kids so I can at least ID the name with the child and I can either ask them or their parent in person before I need an RSVP. It isn't totally accurate but a less rougher estimate than not.