9758/2021/P2/Q07

When performing a trick a magician says the word ABRACADABRA. The 11 letters of this word are arranged in a row.
(a) Find the number of different arrangements that can be made.

[2]

(b) Find the number of different arrangements in which the $2 \mathrm{~B}$ ‘s are next to each other, the $2 \mathrm{R}$ ‘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]

(c) Given that the 11 letters are arranged randomly, find the probability that all $5 \mathrm{~A}$ ‘s are together.

[3]