DiceCombination.java

public class DiceCombination {
	int count;	
	Map<String,Integer> cache = new HashMap<>();
	
	public float sumPossibilityButtomUpDP(int dice, int target) {
		int total = (int) Math.pow(6,dice);

		int[][] dp = new int[dice+1][target+1];
		for(int i = 1; i <= Math.min(target,6); i++) {
			  dp[1][i] = 1;
		}
		for (int i = 2; i <= dice; i++)
	      for (int j = 1; j <= target; j++)
	          for (int k = 1; k <= 6 && k < j; k++) 
	            	dp[i][j] += dp[i-1][j-k];
	            
		return (float)dp[dice][target]/total;
	}
	
	public float sumPossibilityTopDownDP(int dice, int target) {
		int total = (int) Math.pow(6,dice);
		int res = helperTopDownDP(target,dice);
		return (float)res/total;
	}
	
	public int helperTopDownDP(int target, int dice) {
		if(dice == 0) {
			return target == 0 ? 1:0;
		}
		if(cache.containsKey(String.valueOf(dice) + "*" + String.valueOf(target))) {
			return cache.get(String.valueOf(dice) + "*" + String.valueOf(target));
		}
		int res = 0;
		for(int k = 1; k<=6; k++) {
			int tmp = helperTopDownDP(target-k,dice-1);
			res+=tmp;
		}
		cache.put(String.valueOf(dice) + "*" + String.valueOf(target), res);
		return res;
	}
	
	public float sumPossibility(int dice, int target) {
		int total = (int) Math.pow(6,dice);
		helper(target,0,dice, 0);
		return (float)count/total;
	}
	
	public void helper(int target, int trial, int dice, int sum) {
		if(trial == dice) {
			if(target == sum)
				count++;
			return;
		}
		for(int i = 1; i<=6; i++) {
			helper(target, trial+1, dice, sum+i);
		}
	}
	
	public static void main(String[] args) {
		DiceCombination dc = new DiceCombination();
		System.out.println(dc.sumPossibility(10,35));
		System.out.println(dc.sumPossibilityTopDownDP(10,35));
		System.out.println(dc.sumPossibilityButtomUpDP(10,35));
	}
}

From Line 26 to Line 40. I don't think cache works. You only need the "result" variable and the program still works.
Since every recursion loop, dice and target are unique than previous, so map.containsKey() branch will never been entered.