1. Probability Question [URGENT!!!]

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2. Originally Posted by ultimatedemon
I am having a great deal of trouble with one question which I have not been able to solve. I am having trouble picturing the problem. I was wondering if anyone could help me by showing me the steps to solving the problem and with the solution.

QUESTION:
Three molecules of type A, three of type B, three of type C, and three of type D are to be linked together to form a chain molecule. One such chain molecule is ABCDABCDABCD,and another is BCDDAAABDBCC.

(a) How many such chain molecules are there? [Hint: If the three A's were distinguishable from one another -- A1, A2, A3 -- and the B's, C's, and D's were also, how many molecules would there be? How is this number reduced when the subscripts are removed from the A's?

(A1 means A subscript 1, same for A2 and A3)

The final answer isn't important to me, but the steps are. I really want to understand this problem. Please if anyone can help me I would greatly appreciate it. Thank you in advance!
$\displaystyle \frac{12!}{3! \, 3! \, 3! \, 3!}$.

Permutations with Repetition