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.
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