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6. Recall that a Boolean matrix is a matrix whose entries are 0 and 1, and where 0 and 1 are interpreted as "false" and true" respectively, instead of the algebra numerical values (a) How many 10-by-10 (10 rows and 10 columns) Boolean matrices are there? Hint: a 10-by-10 matrix has 100 entries; here each entry may be 0 or only: multiplication principle? (b) How many 10-by-10 Boolean matrices are there that have all ones on the main diagonal? Hin: you only have I choice for the mainagonal hen: how about ihe of- diagonal entries? (c) How many 10-by-10 Boolean matrices are there that are symmetric around the main diagonal? Hint: once the lower part (below main diagonal) is chosen, the upper part is chosen; there is still the man diagonal as well (d) How many 10-by-10 Boolean matrices are there that have 5 ones in the first row and 6 ones in the last row? Hint: count carefully (e How many 10-by-10 Boolean matrices are there that are symmetric around the main diagonal and have exactly 3 ones on the main diagonal