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All I can remember is to work out $6!$ then deal with the last term which can only be A or O but I do not know what to do!

Can anyone please show me with workings and terminology?

Thanks in advance!

Newbie Noob
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    Just say there are $5!$ arrangements ending in $A$ and $5!$ ending in $O$, for a total of $2\cdot 5! = 240$. Alternately, of the $6!$ possible arrangements, exactly $1/3$ end in a vowel. – mjqxxxx Jun 07 '21 at 17:37

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It's easier to first deal with the last placeholder, then the first 5 placeholders. The last placeholder can only be "A" or "O", so that gives 2 choices. And there are $5!$ permutations for the first 5 placeholders. So there are $5!\times 2 = 240$ arrangements in total.

Leo L.
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