( 1)

Suppose that the number of programs in grade two is X, then the number of programs in grade one is (5/6) X.

Suppose the number of programs in grade two is y, then the number of programs in grade one is (7/6) y.

Through the conditions of the topic, simultaneous equations can be obtained:

[y+(7/6)y]-[x+(5/6)x]=(2/ 1 1)*[x+(5/6)x]

(7/6)y-(5/6)x = 2

By solving this set of equations, we can know that x=6 and y=6.

That is to say, there are five freshmen, six sophomores, seven sophomores and six sophomores.

(2)

First of all, it can be determined that the total number of * * * will be 24, and the number of first prizes can be divisible by the number of second prizes, indicating that the number of first prizes can also be divisible by the sum of the number of first prizes and second prizes, that is, 24. At the same time, the number of first prizes cannot exceed the number of second prizes (the number of first prizes can be divisible by the second prizes), so the possible number of first prizes is only a multiple of 24, which cannot exceed half of 24, that is. So the possible situations are 1, 2, 3, 4, 6 and 12. According to another condition, after judging one by one, it can be concluded that the number of first prizes is four.