Question: Let A = {1, 2, 3, 4, 5, 6, 7, 8}. In how many ways can we partition A as A1 A2 A3

Let A = {1, 2, 3, 4, 5, 6, 7, 8}. In how many ways can we partition A as A1 ⋃ A2 ⋃ A3 with
(a) 1, 2 ∈ A1, 3, 4 ∈ A2, and 5, 6, 7 ∈ A3?
(b) 1,2 ∈ A1, 3, 4 ∈ A2, 5, 6 ∈ A3, and |A1| =3?
(c) 1, 2 ∈ A1, 3, 4 ∈ A2, and 5, 6 ∈ A3?

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