Suppose that 14 school children line up in random order up for a vaccine, 2 in grade 1, 6 in grade 2, 2 in grade 3 and 4 in grade 4 in such a way that all arrangements are equally likely.

1) What is the probability that the child at the front of the line and the child at the end of the line are in the same grade?

2) What is the probability that all of the grade 1 children are in the first half of the line? (i.e. in the first 7 places).