A middle school basketball team has two types of spare jerseys left in the equipment bag: some have the number \(3\) on them, and others have the number \(6\) on them. The bag contains more than five jerseys of each type. During practice, five players line up side-by-side for a photo. Each player puts on one jersey, creating a \(5\)-digit number when read from left to right. The coach wants this \(5\)-digit number to be a "lucky number", which means it must be divisible by \(9\).
How many different \(5\)-digit "lucky numbers" can the players form using only the spare jerseys from the equipment bag?
Did You Know?
If the sum of the digits of a number is divisible by \(9\), then the number is divisible by \(9\). If the sum of the digits of a number is not divisible by \(9\), then the number is not divisible by \(9\).
For example, the number \(10\,278\) is divisible by \(9\) since the sum of the digits is \(1+0+2+7+8= 18\), which is divisible by \(9\). However, since the sum of the digits of the number \(12\,345\) is \(15\) and \(15\) is not divisible by \(9\), then the number \(12\,345\) is not divisible by \(9\).
Theme: Number Sense