Mathematics

No. of all possible arrangements = 11!/(2! x 2!) = 9979200

since in 11 letters, there are 2 B's and 2 I's

Instead, we can count the no. of arrangements that 2 B's are together, i.e. we can treat it as if there were 10 letters in which 2 are the same (the 2 I's)

So no. of poss. arrangements that 2 B's are together is:

10!/2! = 1814400

Hence no. of possible arrangements that the B's are separated is:

9979200 - 1814400 = 8164800