A bank wants to allow customers to use personal identification numbers $($PINs$)$ for their ATM which are six characters long, using hexadecimal characters instead of only decimal digits. The hexadecimal system includes $16$ characters, with the decimal values $09$ and the letters AF$.$ a$.$ How many different PIN combinations are possible if no character can be repeated and the characters must alternate between letters and numbers?$$ Hint: you could start with either a letter or a digit.