In how many ways, can the letters of the word ALGEBRA be rearranged with condition: the two As never appear next to each other.
The way I think of a solution is: total number of permutations of the word ALGEBRA (accounting for the two As) - the total number of permutations of the word ALGEBRA where the two As do occur together.
The answer stood out to be 1800. Can someone confirm this?
EDIT: elaborated solution - 1. total number of permutations of the word ALGEBRA with the two As accounted for: 7! / 2! = 2520 2. total number of permutations of the word ALGEBRA with the two As always occurring together("AA",L,G,E,B,R being the distinct elements): 6! = 720
hence answer is 1 minus 2 i.e 1800.