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There are two copies of the letter A and an unlimited supply of the letters...

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There are two copies of the letter A and an unlimited supply of the letters B, C, and D. How many words of length 10 can you make from these, such that: both A's are used and the 3rd letter is an A and there is no B appearing between the A's ? Hint: Consider the two cases: (i) the A in the third position is the first A in the word, and (ii) it is the second A

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