N2021 P2 Q7

When performing a trick a magician says the word ABRACADABRA. The \(11\) letters of this word are arranged in a row

1. Find the number of different arrangements that can be made.[2]
2. Find the number of different arrangements in which the \(2\) B’s are next to each other, the \(2\) R’s are next to each other, exactly \(4\) of the A’s are next to each other, and the C is next to the D.[3]
3. Given that the \(11\) letters are arranged randomly, find the probability that all \(5\) A’s are together.[3]