problems separating class and source files

In my _Mathematics package. I've separated the source files into bin and src folders like so:

_Mathematics ->

    Formulas ->

       src ->

           // source files containing mathematical formulas...
           // Factorial.java 

       bin ->

           // Factorial.class
           // class files containing mathematical formulas...

   Problems ->

       src ->

           // Permutation.java
           // source files containing mathematical problems...

       bin ->

           // Permutation.class
           // class files containing mathematical problems...

But, when I compile the file with main(), there is an error like so:

Exception in thread "main" java.lang.NoClassDefFoundError: _Mathematics\Problems
\bin\Permutations (wrong name: _Mathematics/Problems/bin/Permutations)
        at java.lang.ClassLoader.defineClass1(Native Method)
        at java.lang.ClassLoader.defineClass(ClassLoader.java:792)
        at java.security.SecureClassLoader.defineClass(SecureClassLoader.java:142)
        at java.net.URLClassLoader.defineClass(URLClassLoader.java:449)
        at java.net.URLClassLoader.access$100(URLClassLoader.java:71)
        at java.net.URLClassLoader$1.run(URLClassLoader.java:361)
        at java.net.URLClassLoader$1.run(URLClassLoader.java:355)
        at java.security.AccessController.doPrivileged(Native Method)
        at java.net.URLClassLoader.findClass(URLClassLoader.java:354)
        at java.lang.ClassLoader.loadClass(ClassLoader.java:424)
        at sun.misc.Launcher$AppClassLoader.loadClass(Launcher.java:308)
        at java.lang.ClassLoader.loadClass(ClassLoader.java:357)
        at sun.launcher.LauncherHelper.checkAndLoadMain(LauncherHelper.java:482)

Here's the Permutation.java file, where main() is located.

package _Mathematics.Problems.bin;
import _Mathematics.Formulas.bin.Factorial;

public class Permutations {
    public static void main(String args[]) {
        System.out.printf("There are 10 students. Five are to be chosen and seated in a row for a picture.%nHow many linear arrangements are possible?%n" + 
            (new Factorial(10).r/new Factorial(5).r) + "%n%n");
        System.out.printf("How many permutations are there in the word 'permutation'?%n" + 
            new Factorial(11).r + "%n%n");
    }
}

And here is the other file I have, Factorial.java:

package _Mathematics.Formulas.bin;

public class Factorial {
    public int o;
    public long r;
    public Factorial(int num) {
        long result = 1;
        for(int i = num; i > 0; i--)
            result *= i;
        this.o = num;
        this.r = result;
    }
}

Should I keep the package _Mathematics.Problems.bin;, or should I change it to package _Mathematics.Problems.src;?

What is wrong with my code??

Help would be much appreciated.

Solution

Two issues worth mentioning:

bin directories are normally used for executable files. This is because (generally) your OS will have an environment setting that points to these directories, so when you try to run a program, it knows where to look. When you run a Java program, Java itself is the executable (your OS needs to know where to find it). The OS doesn't need to find your actual Java class files, Java needs to find them, for which it uses a completely different environment setting (the classpath). Because of this, if you're putting Java class files in a bin directory, you're probably doing something wrong.

Secondly, your package structure (_Mathematics.Problems.bin) should match exactly the directory structure, but it should reflect the purpose of the classes, so _Mathematics and Problems are reasonable parts of a package structure, but, again, bin or src, is not. Normally, I would create classes and src directories and then my package structure begins under there

So, as explained above, to fix the issue:

make sure the directory and package structures are identical for your src and classes
by removing the bin part of your package structure, this will be easier.