In this problem, we are concerned with two dimensional arrays (matrices) that have 20 rows and 20 columns; further, each entry is a member of {1, 2, 3}.
How many such matrices are there in each of which
(a) among the 100 entries in the first 5 rows, exactly 30 are ones (and there are no other restrictions)?
(b) every row has exactly 5 ones and also exactly 5 twos?