Test.java

import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;

public class Test {
   private static final int CLUMP = 10;
   private static BigInteger[][][] results;;

   private static BigInteger foo(int ones, int zeroes, int minTrailing) {
       if (ones<CLUMP || zeroes<0) return BigInteger.ZERO;
       BigInteger result = results[ones][zeroes][minTrailing];
       if (result!=null) return result;
       result =
           foo(ones-1, zeroes, Math.max(0, minTrailing-1)) // set C
           .add(binomialCoefficient(ones+zeroes-CLUMP, zeroes)) // set D
           .subtract(foo(ones-1, zeroes, CLUMP-1)) // set E
       ; // set B
       if (minTrailing==0) result = result.add(foo(ones, zeroes-1, 0)); // set A
       results[ones][zeroes][minTrailing] = result;
       System.out.println("f("+ones+","+zeroes+","+minTrailing+") = "+result);
       return result;
   }

   private static BigInteger binomialCoefficient(int m, int n) {
       BigInteger result = BigInteger.ONE;
       n = Math.max(n, m-n);
       for (int i = m; i>n; i--) result = result.multiply(new BigInteger(Integer.toString(i)));
       for (int i = m-n; i>0; i--) result = result.divide(new BigInteger(Integer.toString(i)));
       return result;
   }

   public static void main(String[] args) {
       int ones = 128;
       int zeroes = 288;
       results = new BigInteger[ones+1][zeroes+1][CLUMP];
       BigInteger clumpWays = foo(ones, zeroes, 0);
       BigInteger ways = binomialCoefficient(ones+zeroes, ones);
       System.out.println("With "+ones+" ones and "+zeroes+ " zeroes,");
       System.out.println(clumpWays+" ways with clumps of "+CLUMP+" out of ");
       System.out.println(ways+" ways");
       System.out.println("= "+new BigDecimal(clumpWays).divide(new BigDecimal(ways), MathContext.DECIMAL32)+" chance");
       System.out.println("or 1 out of "+new BigDecimal(ways).divide(new BigDecimal(clumpWays), MathContext.DECIMAL32));
   }
}