Small World

In one of our shows we pull up a volunteer based on their birthday. Yesterday I called for a May baby as we normally go with whichever month is upcoming. When my volunteer told me his birthday was May 7th, i pointed out that it was 4 days before MY birthday, May 11th, at which point the first teacher on stage-left started wildly waving her hand - that was her birthday as well. We air high-fived, of course. About 10 minutes later we called up another volunteer; it turns out her name was Nicole. There were more high-fives about Nicoles genetically being chemical geniuses. As volunteer Nicole was leaving stage she whispered to me "My birthday is May 11th." WOW What is the probability that in a room of 230 people, three of them have the same birthday AND that all three are female AND that 2 of the 3 would have the same name? That's mind wobbling.