What do you mean by number of ways? 
A = 1(1), 1(2), 2
B = 1(3), 3.
a(b) - means - that there is an element with value a but with unique id b
if there is only one element with such value, skip brackets.

Here are the possible results of merging (using operator < for the values)

1(1); 1(2); 1(3); 2; 3
1(1); 1(3); 1(2); 2; 3
1(2); 1(1); 1(3); 2; 3
1(2); 1(3); 1(1); 2; 3
1(3); 1(1); 1(2); 2; 3
1(3); 1(2); 1(1); 2; 3

So, the answer will be something like  P(1)! * P(2)! * P(3)! ... * P(n)! 
where P(k) means - amount of elements with value = Array[k].

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