If there are more than 26 kids in the group, you can tell them you know for sure that two of them have names starting with the same letter (more than 12: birthday in the same month, and so on). In a column in the newspaper, the physicist Robbert Dijkgraaf recounted how he did this once with a group of five or six year olds; one of them got it immediately, and a lively discussion followed.

From there, you might try to explain the pigeonhole principle, or go on to counting, or even do the thing about people knowing each other at a party (though that might be too hard).

Good luck!