Solution of the Week #288 - Round Table

There are 64 (2^6) possible gender permutations of the six children. For all the males to be seated together, all of the girls need to be older than all of the boys, and there is one such arrangement for each of the possible numbers of girls from 0 to 6, giving 7 possible valid arrangements.

Therefore the probability is 7/64, which is just under 11%.