Assume that the classes listed in the Java Quick Reference have been imported where appropriate. Unless otherwise noted in the question, assume that parameters in method calls are not null and that methods are called only when their preconditions are satisfied.
In writing solutions for each question, you may use any of the accessible methods that are listed in classes defined in that question. Writing significant amounts of code that can be replaced by a call to one of these methods will not receive full credit.
This question involves computing factorials and using factorials to compute the number of possible ways that items can be selected from a group of choices. You will write two methods in the Combinatorics class that follows.
public class Combinatorics
{
/** Precondition: n is between 1 and 12, inclusive.
* Returns the factorial of n, as described in part (a).
*/
public static int factorial(int n)
{ /* to be implemented in part (a) */ }
/** Precondition: n and r are between 1 and 12, inclusive.
* Determines the number of ways r items can be selected
* from n choices and prints the result, as described in part (b).
*/
public static void numCombinations(int n, int r)
{ /* to be implemented in part (b) */ }
}
In mathematics, the factorial of a positive integer n, denoted as n! , is the product of all positive integers less than or equal to n.
The factorial of n can be computed using the following rules.
Case I: If n is 1, then the factorial of n is 1.
Case II: If n is greater than 1, then the factorial of n is equal to n times the factorial of (n - 1).
The factorial method returns the factorial of n, as determined by case I and case II. Write the factorial method below. You are encouraged to implement this method recursively.
/** Precondition: n is between 1 and 12, inclusive.
* Returns the factorial of n, as described in part (a).
*/
public static int factorial(int n)