Question

(1 point) A Discrete Mathematics student comes from the village of BALLYGOBACKWARDS. As an hilarious jape, on the way home from a late- night study session, he decides to rearrange the letters on one of the sign-posts. How many arrangements of the letters in BALLYGOBACKWARDS are possible? Answer: 8.71783e11 Of these arrangements, how many have all the L's together? Answer: Of these arrangements, how may have all the letters in alphabetical order? Answer: Note: You can earn partial credit on this problem.

Answer 1

How many arrangements of the letters in BALLYGOBACKWARDS are possible?
There are a total of 16 letters. There are 2 Bs, 2 Ls and 3 As. So, the number of arrangements possible is 16!/(2!x2!x3!) = 8.71783e11.

Of these arrangements, how many have all the Ls together?
Let us count the 2 Ls as a single letter. So, we have a total of 15 letters. There are 2 Bs and 3 As. Since the Ls are indistinguishable, we do not have to consider them. So, the number of arrangements possible is 15!/(2!x3!) = 1.08973e11.

Of these arrangements, how many have all the letters in alphabetical order?
Since the word has only alphabets, there is only 1 possible arrangement where all the letters will be in alphabetical order.