how many ways are there to arrange $8$ pennies and $5$ nickels in a How can you arrange a line of $8$ pennies and $5$ nickels, so that no $2$ nickels are next to each other (pennies are indistinguishable and nickels are too)?
Answer: I set nickels and pennies next to each other so I get ${9 \choose 5}*8!*5!=609638400$. Is this correct?

_ N _ N _ N _ N _ N _
assume this is the placement which you are looking for .
The blanks have to be filled by 8 pennies and no blank space should be empty except for the first and the last blank. 
the sequence then becomes 
_ N p N p N p N p N _ 
now you are remaining with 4 pennies and 6 potential places where they an come.
Since the pennies and the nickels are indistinguishable internal rearrangements do not count.
Can you take it from here?
