# Find the number of arrangements of BANANA

Attempt:

1. If the Ns appear next to each other

I treat as if there is 1 B, 3 As, 1 N which leads to $\frac{5!}{1!3!1!}$

1. Every N is followed by an A

I count the possible "unique characters" as NA-2, A-1, B-1 so I end up with $\frac{4!}{2!}$

1. the two Ns must be separated

No matter how much I think about it, I'm not sure I can get an answer that doesn't lead me with a headache.

$\frac {6!}{3! × 2!}$ to arrange alphabets of BANANA.