How many ways can the letters of the word BANANA be arranged so that no two a come together?

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In how many ways can the letters of the word BANANA be rearranged such that the new word does not begin with a B?

What I did is incorrect. I said there are $5$ choices for the first place and then $5!$ possibilities after that for a total of $5\cdot5!=600$. However, I think I need to divide by $2$ and $3$ because of the repetitions of N and A. So how many ways can I do this? What am I missing?