Due: Saturday, July 1

Please upload your source code files using CSNS. Note that file uploading will be disabled automatically after 11:59PM of the due date, so please turn in your work on time.

1. The number of different combinations that can be made by choosing m objects out of n objects is usually denoted as C(n,m), and can be calculated with the formula C(n,m) = n! / ( m! * (n-m)! ). For example, C(4,2) = 4! / (2! * (4-2)!) = 4 * 3 * 2 * 1 / ( 2 * 1 * 2 * 1 ) = 6. Write a Java program which does the following:

• (10pt) Gets two positive integer numbers n and m from user input. You should use Scanner for input.
• (15pt) Checks whether the input is correct, namely, whether both numbers are greater than 0 and n is no less than m. If the input is not correct, output an error message, and ask the user to re-enter the two numbers. Repeat this process if necessary until the program gets the right input.
  
• (15pt) Implements a method to calculate factorial, and use this method to calculate C(n,m)
• (5pt) Outputs the result in the form "C(n,m) = value", for example, C(4,2) = 6 if n is 4 and m is 2.
  

2. (25pt) Implement a recursive binary search method, and write a Java program to test your method.