There are 10 letters - a, b, c, d, e, f, g, h, n, g. I...
There are 10 letters - a, b, c, d, e, f, g, h, n, g. I have to arrange them in a way that "a" wouldn't be near "c" and also "a" wouldn't be near "g" How many possible combinations are possible? How to solve it mathematically?
Homework Answers
We have 10 letters of which be arranged in 10! / 2! = 1814400 ways ( since "G" comes twice)
Now to arrange them in such a way that "A" wouldn't be near "C" and also "A" wouldn't be near "G".
Now assume that "AC" is a single letter. So that we now have 9 letters. we can arrange these 9 letters in 9!/2! ways. Now A & C can be arranged as AC & CA, so end up having 2 x 9!/2! = 9! arrangements where A & C appear together.
Similarly wehave 9! arrangements where A & G appear together.
So, the arrangement that "A" wouldn't be near "C" and also "A" wouldn't be near "G" = 10!/2! - 9! - 9!
= 1088640 ways
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