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When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule.
It goes like this:

If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....]

So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:
There are 11 letters in total
There are 4 identical I's
There are 4 identical S's
There are 2 identical P's
So, the total number of possible arrangements = 11!/[(4!)(4!)(2!)]
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In the given question, we want to arrange the following: A, B, B, C, C
There are 5 letters in total
There are 2 identical B's
There are 2 identical C's
So, the total number of possible arrangements = 5!/[(2!)(2!) = 30

Answer: 30

Cheers,
Brent